First Minister Alex Salmond said Scotland's future was in Scotland's hands, as counting continued in the independence referendum.
With turnout expected to be extremely high, senior members of both the Yes and No camps were focusing on the historic nature of the vote.
Mr Salmond tweeted: "This has been a remarkable day. Scotland's future truly is in Scotland's hands."
Earlier, SNP deputy leader Nicola Sturgeon hailed the ballot as "an amazing, emotional, inspirational day of democracy".
Labour's leader in Scotland Johann Lamont said that voters north of the border had cast "the most important votes of our lives".
Ms Lamont said: "Today the people of Scotland have cast the most important votes of our lives. Thank you to everyone who has worked for a No today."
And Ms Sturgeon tweeted: "So that's that. Polls have closed. What an amazing, emotional, inspirational day of democracy this has been. Now we wait."
Blair McDougall, the Better Together campaign director, welcomed the high turnout, which was widely predicted to top the 83.9% recorded in the 1950 general election - the highest in the UK since the introduction of universal suffrage in 1918.
Mr McDougall told Sky News he believed a No vote would be revealed over the course of the night.
He said: "I think there has been an extraordinary turnout tonight - near 100% turnout in some places.
"I think it's great for Scottish democracy, it could be great for Scotland. I think there will be a strong No vote and I think it will mean a better future for people in Scotland."
Scottish Secretary Alistair Carmichael told Sky News: "It looks like we have a good turnout, that's important.
"It has been on the Yes side quite in your face and I have had people coming to me on the doorstep and in the streets saying, whispering almost, 'I'm voting No, I'm on your side'.
"But because the Yes campaign have been so in your face, and you have had some quite sinister points in this campaign - you had the 1,000 people trying to influence the BBC on Sunday night, you had Jim Sillars, one of the most senior people in their campaign talking about there being a day of reckoning.
"What we have got now is a timetable that makes it clear the extra powers we all know the Scottish Parliament needs to finish the process of devolution, which then unlocks the door to constitutional reform across the whole of the United Kingdom, will definitely be delivered."
The chairman of Yes Scotland said he was not conceding defeat, despite a YouGov survey suggesting that Scots have rejected independence by a margin of 54%-46%.
Former Labour MP Dennis Canavan told Sky News: "I'm still optimistic ... I'm not at this stage conceding the result."
Mr Canavan said it was "probably correct" that today's vote would settle the independence question for a lifetime.
He said while the Yes camp had fought a "very positive campaign, a magnificent campaign", the No message was characterised by "a bit of negative scaremongering going on, a bit of collaboration, perhaps even collusion, on the part of the British establishment".
Liberal Democrat MP for Gordon and No supporter Sir Malcolm Bruce said he believed that "reality has kicked in" with voters switching back to No after being briefly seduced by the Yes campaign's message.
Sir Malcolm said: "Certainly we felt that the campaign was swinging back to our side - if it ever really swung away to the extent that people suggested - both in terms of our canvassing and the responses we've been getting as people came out of the polling stations.
"I will be very well satisfied if the campaign to keep Scotland in the UK has succeeded. I believe it's in the best interests of Scotland and the UK that that should happen."
With two Scottish Nationalist parliamentarians - Angus MacNeil MP and Alasdair Allan MSP - the Western Isles is expected to have one of the largest turnouts in Scotland and to far exceed the General Election figure of 66.1 per cent in 2010, when there were five candidates.
Out of an electorate of 22,908, the turnout for postal votes including postal proxies was 5,125, which represents almost 90%.
Dr Allan, who led the Yes Camapign, said during the count: "It has been a closely fought campaign both nationally and in the Western Isles. We have fought a long and positive campaign against an absolute onslaught of fear-mongering by the UK Government and their friends in the national media. I hope the Western Isles will chose a better future for Scotland."
Liberal Democrat Deputy Prime Minister Nick Clegg said in a tweet: "The people of Scotland have cast their votes. I sincerely hope that they remain a part of our family of nations."
Former Liberal leader Lord David Steel told Sky News: "Nearly half of Scotland is going to be disappointed with the result whichever way it goes.
"Therefore, there is an obligation on the politicians to take that into account and to be very mindful and sensitive to half the population who have not voted for the result.
"I think it is very important they don't just talk about greater powers for the Scottish Parliament, but they have got to talk to look and see how they reorganise the United Kingdom."
Michelle Thomson, managing director of the pro-independence Business for Scotland campaign, said the Yes campaign would respect the result of the ballot, even if it meant continued membership of the UK.
She told Sky News: "This is all about the settled will of the sovereign people of Scotland, and if that is what they express, then of course the wider Yes campaign will accept that. That's the whole point.
"Really, then the emphasis will be on Westminster to make good the promises they've made within the timetable they have set out.
"Certainly Scotland will move forward together, there will be a tomorrow, we will continue to be the best of friends."
At the count in Glasgow, Patricia Ferguson, Labour MSP for Maryhill and Springburn said: "I think it's exciting but nerve-wracking.
"It's been a very, very long campaign and today has already been a long day and it's not quite over yet.
"I think everyone will be glad to get the result and move on."
Former Scottish Secretary Michael Moore, the Lib Dem MP for Berwickshire, Roxburgh & Selkirk, told Sky News: "In the last couple of weeks, the arguments about the NHS and other aspects of public services in Scotland which are fully devolved already became very serious parts of the campaign.
"If we are candid, I don't think at all times we were smart enough and quick enough to respond to those particular points.
"But there is a real desire it seems to me for change and the importance for all of us on the Better Together side is that the commitments we made in recent times, about further devolution to Scotland, if we stay part of the UK, those have to be delivered and quickly."
SNP national women's officer Tasmina Ahmed-Sheikh, a member of the Yes Scotland advisory board, said "Scotland has won" whatever the outcome.
"The polls have spoken but we will see what the people of Scotland have said," she said.
"We absolutely believe in the democratic will of the people of Scotland, and that will prevail, so I think we will just wait for the actual result when it comes through.
"What we are seeing is a massive engagement of people across the country, and I find that really refreshing.
"People coming up from 7am, unheard of queues at polling stations, so I think that says an awful lot.
"I think at the end of the day Scotland has won, without a doubt, whatever the outcome, simply because we have got so many people now interested in the future of this country."
Liberal Democrat leader in the House of Lords Jim Wallace said: "Never write Alex (Salmond) off... it's not for me to say what he should do.
"He'll have some hard thinking to do. I think he will be in a difficult position - he has led his troops to the top of the hill, it's difficult to march them down again."
Actress, comedian and Yes campaign advisory board member Elaine C Smith said of the referendum campaign: "People have something to vote for.
"The argument, the engagement, I love the fact that people in pubs are talking about what currency we're using and what we're going to do with the National Health Service, and not just going 'we'll leave it to those guys in suits'.
"I feel very grateful to be alive and to be part of this - even though I'm knackered."
Speaking at the Edinburgh count, Green MSP Alison Johnstone said: "I have been chatting to campaigners and activists on both sides - obviously there is a great deal of interest but there is a long night ahead.
"Obviously there was a YouGov exit poll earlier on, but we will wait and see. I think it is too early in the evening to say one way or the other.
"It is really exciting - the fact that the campaign has engaged so many people. It has got people who have never been involved in politics involved. It has been a successful campaign in those terms certainly."
There were also early appearances at Ingliston from Yes Scotland chairman Dennis Canavan, Lib Dem MP Sir Menzies Campbell, and fellow Lib Dem and Advocate General for Scotland Lord Wallace.
After the first result saw No win Clackmannanshire by a margin of 54% to 46%, Labour's former Cabinet minister Lord (John) Reid told BBC News: "I'm delighted that we've won the first to be announced. I think it was quite a clear victory, but it's one and there are another 31 to go.
"I'm sure we'll win some and lose some, and it will probably be some hours before the pattern emerges, but to win by about 10% I think is gratifying."
Labour MP Thomas Docherty said he is confident No will win in Fife, after seeing samples of the votes being taken out of ballot boxes and postal votes.
The Dunfermline and West Fife MP told BBC News: "What's very clear tonight is that Fifers have said No. We don't obviously have the final figure and we're some time away from having that, but it looks like Fife has voted No tonight.
"We've had very, very strong results in some places. We've won almost every polling district in Dunfermline and West Fife and every polling district in North East Fife and it's quite clear that some of those margins that we have been stacking up look very nice indeed tonight."
Scottish Labour deputy leader Anas Sarwar, MP for Central Glasgow, said: "It's been a very encouraging start for us but we've still got a long night ahead.
"What we are all struck by, whether Yes or No campaigners or supporters, is the incredible turnout that we've seen in this referendum campaign.
"The challenge for all of us is to tap into that real desire for change and to take on the task of unifying our country whatever the result, and bringing people together to create a better future for ourselves and for future generations.
"Our country is divided. We've got to make sure we bring people together."
He said on the Glasgow turnout: "Given Glasgow's historic turnouts, turnout today is pretty good, although less than in other places.
"The challenge for all of us is to make sure we keep people engaged in the political process beyond the referendum.
"How do you do that? It's by recognising that our politics is broken and our economy is broken. And we've got to fix them both."
Dennis Canavan, chairman of Yes Scotland, said: "I am conceding nothing at this stage because less than a handful of local authorities have declared so far, and these local authorities are not exactly a representative body of Scotland, in the sense that they are very, very small populations.
"We could have, say, one big local authority declaring in the next hour or so and we could be running neck and neck again.
"So at this stage I am still optimistic, I am still hopeful, and we will see how it goes."
Speaking from the Edinburgh count, Scottish Socialist Party spokesman Colin Fox, a key figure in Yes Scotland, said tonight's result looks likely to be "independence deferred".
The unionist parties will "rue the day" if they fail to deliver meaningful new powers to Scotland, he added.
"We're looking forward to some Yes victories in Glasgow and Dundee and perhaps elsewhere, and I think that will be welcome news," he said.
"The big story tonight is the astonishing levels of turnout in a political contest in Scotland, which is on a par with North Korea, China, Cuba and those places.
"I think it's remarkable and I certainly want to pay tribute to the Yes campaigners who over the last two years have energised this country. Clearly both sides of the campaign deserve credit for those levels of turnout."
Commenting on the relatively lower turnout in Glasgow in comparison with other areas, Mr Fox said: "Glasgow's turnout in the Scottish Parliament elections is usually 40% and it is now 75%, so that's not to be sniffed at.
"Let's hope we can keep it at that level, I think it's astonishing. Nearly doubling the turnout in Glasgow is a significant achievement for Scotland's biggest city, with the greatest deprivation and the biggest social problems."
He added: "In the last 10 days the British political establishment threw everything including the kitchen sink at the people of Scotland, every threat imaginable.
"Every propaganda trick was used and it's clearly had an effect. They've frightened people. The elderly and the middle class are largely the No voters tonight, and the working class people across Scotland we will find in huge numbers backed the Yes campaign.
"Today, the choice has been between independence and independence deferred, and it looks like we are going to get independence deferred.
"I don't think these three parties have got anything in common with these new powers. They're phantoms, they're mythical, and I think if they don't deliver meaningful powers if we get a No vote then I think they will rue the day."
The Yes campaign has demonstrated the social democratic and socialist values of a large number of Scottish people, which "has got to be good for the future of the left".
He added: "We rejected the xenophobic, warmongering, dog-eat-dog, devil take the hindmost politics of Westminster and so have an enormous proportion of the Scottish population."
Former Scottish Socialist MSP Tommy Sheridan told the BBC: "I am feeling almost broken-hearted. I feel that the British establishment has mobilised the big guns, they've mobilised the bankers, they've mobilised the billionaires, they've mobilised the supermarkets.
"They've all been corralled into Number 10 to get out there and give their warnings and frighten people and I think people have been frightened, people have been genuinely frightened by some of the threats that have been issued."
Labour MP Jim Murphy, who played a leading role in the Better Together campaign, told Sky News: "Having spent two long years emphasising our differences, we have now got to talk about what Scots, everyone here, has in common in bringing the country back together and make a success of what has been a remarkable turnout.
"We are going to have to make a success of the decision Scotland has made. While I'm delighted, there is no time or space for triumph and we have got to get on and offer that devolution package we offered and unite the country around that.
"I always had great faith in the common sense of the people of Scotland. Of course, there were one or two polls who had the Yes campaign ahead. That just made us work harder, made us campaign even more strongly.
"While many people were willing to give the SNP the benefit of the doubt, they had enormous doubts about things like the currency or separate armed forces."
In his first public comment since the results started coming in, Mr Salmond tweeted: "Well done to Glasgow, our Commonwealth city, and to the people of Scotland for such incredible support."
Prime Minister David Cameron said: "I've spoken to Alistair Darling - and congratulated him on a well-fought campaign."
Douglas Alexander, the shadow foreign secretary and key player in the Better Together campaign, told Sky News: "We have made a conscious decision here in Scotland for the faster, better, safer change that we were offering and to reject separation and the break up of the United Kingdom.
"I think there needs to start today a process of reconciliation. Our challenge is to bring our nation together and take our nation forward."
Labour former Scottish secretary Lord Reid, speaking to BBC Radio 4's Today programme, said he believes a substantial proportion of the Yes vote wanted "positive independence" while a substantial number also made a protest vote and may not necessarily have supported separation.
He said he believes the latter group are against austerity, cutbacks, disillusioned against politicians and "some are against the English, hopefully not a lot of them".
Lord Reid went on: "Normally in a general election they are spread across six parties. But in this occasion they are all under one flag because this is the way they can express their view.
"Does that mean we can ignore that? No, because there is certainly the demand for more powers and I actually support more powers to the Scottish Parliament because it makes it more responsible apart from anything else.
"But there's also a problem of disillusionment and alienation, which is not only Scottish and therefore this has implications for England as well."
He added: "I say to Alex Salmond and Nicola Sturgeon, don't bring this up again, you promised you wouldn't. Let's get on and address the sort of problems raised."
Referring to what he would like Mr Salmond to say, Lord Reid said: "Let's hear the words: 'I accept the decision of the Scottish people and the mandate to remain within the United Kingdom, now let's get together to make it work better.'"
The leader of the Better Together campaign, Alistair Darling, said in a tweet: "An extraordinary night. Humbled by the level of support and the efforts of our volunteers. Will give speech in Glasgow shortly."
In a tweet, Mr Cameron added: "I'll be making a statement following the Scottish Referendum results just after 7am."
Yes supporters spent the night outside the Scottish Parliament still hoping for a result that looked increasingly unlikely as dawn approached.
Piper Chris Davidson, 39, revived their ebbing spirits with Flower Of Scotland and When The Saints Come Marching In, which sparked an outbreak of singing and dancing.
But there was disappointment among the mainly young crowd, who were watched closely by police and TV crews from around the world. While some were angry after a long night of hope, others wept as the results came through.
Mr Davidson, a former soldier, said: "Yes or No, we have to work together."
Talking about the promised extra powers the No campaign offered, he added: "If there's lies again, the next vote for independence will be a resounding Yes."
Scottish Labour Party leader Johann Lamont said the result was "decisive".
On whether it had been a happy night, she told Today on BBC Radio 4: "I'm not sure if the word is happy that I'd use, it's very emotional - it's a very emotional time.
"I've seen my country divided and I know there are people out there who are really hurting because they've lost, and we are pleased Scotland has decided it wants to stay in the United Kingdom and I feel it's an affirmation of a size we can move on from.
"When Nicola Sturgeon said on a personal level she was disappointed I can understand that because I know she fought a hard campaign ... she also said this was a vote for change, I absolutely agree with that.
"We know there'll be a debate around powers and constitutional change but I yearn for the arguments around social justice and equality to get back into the stage in the Scottish parliament and elsewhere, engage with people about what it was they wanted when they voted yes and no, and I think we can come together round that."
Former Conservative Party vice-chairman Andrew Rosindell said it was a "fantastic result for Britain", although he warned that improvements to how the UK as a whole is governed should not be rushed to prevent a potential further Scottish referendum.
The MP for Romford told the BBC: "The United Kingdom stays together - the challenge now is of course to work out where we go from here.
"Politics I think has changed forever and we need to respond to that."
He went on: "I think what we need to do is make the right decisions for the long-term future of our country. If we rush into something and don't consider all the long-term implications I fear that by putting a sticking plaster over something, you may finish up with another Scottish referendum in a few years' time, and that's something we want to avoid.
"We need a permanent solution, a new settlement for the whole of the British family."
Mr Rosindell said a decision over whether to recall Parliament is up to the Prime Minister, although added: "I think probably yes it should."
Conservative MP Bernard Jenkin said Mr Cameron needed to deal much more with his MPs as they represent large parts of England.
Asked if he was glad the union had been saved, he told the BBC: "I'm mightily relieved but very concerned that this episode has thrown the whole of the UK constitution into a state of flux rather than settled anything.
"And you can hear Alex Salmond teeing things up for the next row with Westminster because we've really no idea what these promises of extra powers actually are or what is meant by honouring the Barnett Formula and I think all the noises coming out from the briefings of Downing Street are right - we need also to address the answer to the English question, it's no longer the West Lothian question."
The Harwich and North Essex MP went on: "Whatever the promises made are they have to be honoured and we have to respect that a lot of Scottish people voted for separation and that's all got to be addressed.
"But what is right for Scotland is also right for England and I think the Prime Minister should engage much more with his MPs because in fact his MPs represent a majority of constituencies in England."
Archbishop of Canterbury Justin Welby said: "Over the past few weeks the campaign has touched on such raw issues of identity and been so closely fought that it has generated profound questioning and unsettlement far beyond Scotland.
"The decision by the Scottish people to remain within the United Kingdom, while deeply disappointing to many, will be welcomed by all those who believe that this country can continue to be an example of how different nations can work together for the common good within one state.
"This is a moment for reconciliation and healing not rejoicing or recrimination. Some of the wounds opened up in recent months are likely to take time to heal on both sides of the border.
"The historically close relationships that have existed between the Scottish Episcopal Church, the Church of Scotland and the Church of England and our long involvement in mediation have a contribution to make as our societies not only reflect on the lessons of the referendum campaign but engage in delivering the radical restructuring of the relationship between Scotland and the rest of the United Kingdom for which commitments have been made."