Long-time Sinn Fein colleague Gerry Adams led tributes to Martin McGuinness, describing him as a "passionate republican who worked tirelessly for peace and reconciliation and for the reunification of his country".
Mr Adams posted Irish folk singer Luke Kelly's Song for Ireland along with the tweet "A song for Martin McGuinness. I measc Laochra na n-Gael go raibh a anam dilis", which translates as "Among heroes of Gael he had a faithful soul".
Labour MP for Birmingham Yardley Jess Phillips posted on Twitter: "People can do good and bad, things aren't simple. People should be neither reviled or worshipped. I wish he'd helped my constituents find peace."
But Conservative MP for Mid Bedfordshire Nadine Dorries tweeted: "I hope God forgives this man and grants him a place in heaven - however, it will be hard for many to shed tears upon hearing this news."
In a statement, President of Ireland Michael D Higgins paid tribute to the ex-IRA commander's "immense contribution to the advancement of peace and reconciliation in Northern Ireland".
He said: "The world of politics and the people across this island will miss the leadership he gave, shown most clearly during the difficult times of the peace process, and his commitment to the values of genuine democracy that he demonstrated in the development of the institutions in Northern Ireland.
"As President of Ireland, I wish to pay tribute to his immense contribution to the advancement of peace and reconciliation in Northern Ireland - a contribution which has rightly been recognised across all shades of opinion."
He added: "In addition to his services in public life, as an inclusive believer in community in all its forms he will also be remembered for his warm support for Derry GAA and Derry FC.
"His death leaves a gap that will be difficult to fill. May he rest in peace."
Former Northern Ireland secretary Lord Hain said Mr McGuinness was "absolutely crucial" to the peace process.
"He had the grassroots credibility of a republican leader and former IRA commander, that could enable him, along with Gerry Adams, to take his followers, to take republicans, from the past of terror and horror into a democratic future, which is what he did," Lord Hain told the BBC Radio 4 Today programme.
"Sometimes in the history of conflicts - and, goodness me, the island of Ireland has been involved in centuries of conflict with Britain - you need leaders who can rise above their past and, at that point, Martin McGuinness certainly stood the test and proved to be an indispensable figure."
The Labour former cabinet minister revealed that Mr McGuinness also had an unlikely love of the England cricket team.
"I discovered he was a fan of the England cricket team - this was a hardline republican - but I realised watching the Ashes series on the television in the corner of my office in Stormont Castle that he actually was following the England cricket team, he knew all the players," Lord Hain said.
Good Morning Britain host Piers Morgan tweeted: "RIP Martin McGuinness, 66."
In a later post, he compared Mr McGuinness to former president of South Africa and anti-apartheid activist Nelson Mandela, saying: "Both men renounced violence to forge peace. The comparison is valid."
Former Prime Minister Tony Blair said: "I am very sorry to learn of Martin's death and send his family my deep sympathy and condolences.
"I grew up watching and hearing about the Martin McGuinness who was a leading member of the IRA engaged in armed struggle. I came to know the Martin McGuinness who set aside that armed struggle in favour of making peace. There will be some who cannot forget the bitter legacy of the war. And for those who lost loved ones in it that is completely understandable. But for those of us able finally to bring about the Northern Ireland peace agreement, we know we could never have done it without Martin's leadership, courage and quiet insistence that the past should not define the future.
"After first meeting in Northern Ireland and then again shortly after in Downing Street - an historic meeting, between a British PM and the Republican leadership in the Cabinet room where so much Irish history had been made - he explained at length to me the causes of Republican grievance. I listened. We talked. And as the meeting went on he explained why he thought despite all the grievance there was a chance for peace.
"Over the years - through the arduous negotiation of the Good Friday Agreement - and for the years after it, I got to know Martin well. We met many, many times and as the trust grew between himself, my team, Gerry Adams and their team, so the discussions became increasingly open, frank and therefore productive.
"By the time that extraordinary day arrived in 2007 after almost a decade of hard work where we could witness the - to my generation - incredible sight of he and Ian Paisley sitting down together in Government, the transition of Martin to reconciliator was complete.
"Whatever the past, the Martin I knew was a thoughtful, reflective and committed individual. Once he became the peace maker he became it wholeheartedly and with no shortage of determined opposition to those who wanted to carry on the war.
"I will remember him therefore with immense gratitude for the part he played in the peace process and with genuine affection for the man I came to know and admire for his contribution to peace."
Alliance Party leader Naomi Long expressed her gratitude to the former deputy First Minister's "willingness to work with others" in a Facebook statement.
She wrote: "I want to pay tribute to the hard work and dedication Martin invested as an MLA and as deputy First Minister to serving not only his constituents, but Northern Ireland.
"Whilst our politics were very different and while his past is well documented, the compromises he made, the leadership he demonstrated and his willingness to work with other despite those differences as part of the peace process helped secure the peace we all now enjoy.
"For that, we are grateful and our best tribute to him would be to do all in our power to secure that peace and progress for future generations."
Northern Ireland Secretary James Brokenshire said: "I want to extend my sympathy and sincere condolences to the family of Martin McGuinness at this difficult time.
"Martin's personal journey and the clear influence he had on others in the republican movement were instrumental in shaping political institutions in Northern Ireland founded on exclusively peaceful and democratic means.
"While not forgetting the past, no-one can doubt the essential role he played in helping to secure the power sharing arrangements and political progress in Northern Ireland. Martin's commitment to reconciliation and understanding across communities was a significant factor.
"Whilst passionate and robust in his politics, on a personal level I always found Martin to be thoughtful and reflective and appreciated the personal consideration he showed. The importance of family and his home in Derry shone through.
"Martin will be remembered for his contribution to politics in Northern Ireland and particularly during his near ten years as deputy first minister."
Former Northern Ireland secretary John Reid said: "Martin McGuinness's passing is a sad loss to his family, friends and to Northern Ireland as a whole. He was an indispensable part of the peace process.
"Though Martin remained a staunch Republican, he had the courage to change, to compromise, to abandon violence, to embrace old enemies, to promote reconciliation and he made a massive contribution in shaping a better future for everyone in Northern Ireland."
First Minister of Wales Carwyn Jones said: "Martin was vital in bringing peace to Northern Ireland. I worked closely with him over many years at British Irish Councils, Joint Ministerial Councils and beyond.
"When he spoke, people listened. That presence explains much about how he was able to build bridges across the political divide. My thoughts are with his family and friends today."