Here is a selection of their comments:
"I am disappointed that Martin McGuinness has chosen to take the position he has today.
"His actions have meant that, at precisely the time we need our government to be active, we will have no government and no way to resolve the RHI problems.
"It is clear that Sinn Féin's actions are not principled, they are political.
"Let me make it clear, the DUP will always defend unionism and stand up for what is best for Northern Ireland and it appears from the deputy first minister's resignation letter that is what annoys Sinn Féin the most."
"The UK government has a primary role to provide political stability in Northern Ireland and we'll be doing all we can over the coming days to work with the parties to find a solution to the current situation.
"The position is very clear. If Sinn Féin does not nominate a replacement to the role of deputy first minister, then I'm obliged to call and election of the assembly within a reasonable period.
"I would urge the leaders of the political parties to come together and work together to find a solution to current situation and we'll be doing all that we can with the political parties and the Irish government to that end."
"A reasonable resolution could have been achieved which leads me to believe that this crisis goes beyond RHI and points to a more intractable situation.
"The DUP and Sinn Féin's inability to work together is a fundamental flaw not envisaged in the Good Friday Agreement and will continue to burden the people of Northern Ireland as long as their best interests come second to entrenched party politics.
"Today is a dark day for Northern Ireland. I am truly fearful for our future."
"If this was just about RHI, Sinn Féin would hang in, they would hold the DUP and the first minister to account, they'd take steps to introduce cost controls and they'd support a public inquiry into what went wrong.
"But this is not about RHI - it's about Sinn Féin. We've now had 10 years characterised by disappointment, debacles and scandals.
"They are incapable of governing this country. They cannot see the greater good. The Ulster Unionists fought hard in 1998 to get these institutions up and running. We saw devolution as being for the benefit of the people.
"I don't know what Sinn Féin and the DUP have in mind [following the resignation], but it's very clear they'll do what's good for the parties, not what's good for the electorate."
"It looks like we're heading towards an election and that's happening because of Arele Foster's arrogance.
"But if people want an election, let's have it, because people need to hear that we still have no programme for government and now we have costs spiralling out of control with RHI.
"We also now won't have a public inquiry into all of this. We agree with Martin McGuinness when he tells us the DUP have disrespected the nationalist community. But some people wanted to stand side by side with the DUP, holding their hand.
"If DUP and Féin aren't prepared to hold people accountable for the RHI scandal, lets have the electorate hold them to account."
"This changes nothing.
[It] really is a case of 'any lengths' to avoid doing the job of running the country, setting a budget, preparing for Brexit."
"I've long said mandatory coalition would implode. Today it has. It's time to move on.
"The people of Northern Ireland deserve good government.
"There's no point trying to glue back together something that will never work."
"I'm disappointed at the inability of the two parties to deliver stability to Northern Ireland.
"We've nothing to fear from an election. As one of the parties that highlighted concerns about RHI from the beginning, I believe people will realise the constructive role we have played.
"But I believe and election is not what the people of Northern Ireland want. Today can only be a bad news day for Northern Ireland.
"I hope in a a week's time, we're hearing a better story and that the other parties step up and deliver what's required."
"I think it was an inevitable thing to do and when things become inevitable in politics then it is right for them to happen.
"It was clear to us that there was no mechanism for dealing with the RHI scandal within the machinery of Stormont as it stood.
"I believe that we cannot live any longer with the petition of concern and a number of the other aspects of the machinery of Stormont and we also can't go on without putting right at the centre issues to do with the economy and society which have been marginalised.
"Everybody seems to assume that the DUP is coming back to Stormont with the same strength and numbers, we shall see whether that happens."
"Martin McGuinness has led from the front in the Executive for the last 10 years, defending the integrity of the political institutions and realising the potential of the Good Friday Agreement.
"In spite of the provocation, disrespect and arrogance from the DUP, and the failures of the British government to fulfil its responsibilities over that time, Martin McGuinness has always put the people and the political process first.
"This is in contrast to the DUP who have been acting to undermine equality and partnership.
"The money squandered in the RHI project belonged to unionists as well as other taxpayers.
"It is money which should have been used to end poverty and disadvantage or to build public services. No minister responsible for such bad governance in any other administration would be still in office."
"Arlene Foster took a reasonable approach. I don't think it was necessary to have an election to make sure this was all properly investigated. I believe the fundamentals of the devolved settlement are strong."
"Having remained as positive as we can for as long as we can, there is presently a very deep sense of frustration at the instability which now characterises our political institutions.
"The hope and optimism which greeted the Fresh Start Agreement has dissipated. Business confidence stalled because of the uncertainty regarding Brexit and the change of the US Administration.
"The current political situation adds to this uncertainty and will have a negative impact on economic and social development.
"Meanwhile, the global economy is growing, so too are the economies in the UK and the Republic of Ireland, where they are working on ambitious economic growth plans.
"The sad reality is that Northern Ireland is falling behind, and we need political stability to deliver the ambitious plans set out in the new Programme for Government and Export Matters Action Plan to grow trade."
"The business community is not seeking to comment on the specifics that have given rise to today's events, other than to underline that there has seldom been a more important time for all our citizens to have a strong well-functioning Executive.
"Ahead of the triggering of Article 50, expected in March, Northern Ireland urgently requires strong leadership and representation as the UK negotiates its future relationship with the EU.
"It is vital that our collective voice is heard during this crucial period to achieve the best possible outcome for all of our citizens.
"We have waited for years. The launch of the HIA report is scheduled for 20 January...and now it will gather dust.
"I started this campaign, nine years I am doing this, and now the government collapses on us again. I am angry and hurting for everybody."
"The stability of the devolved institutions in Northern Ireland is more important now than ever, given the challenges presented by Brexit. This needs cool heads and calm leadership.
"A peaceful society, politically stable institutions and a strong economy are intricately bound together.
"The people of Northern Ireland must have confidence that there is a coherent, cohesive and collective government that is open, accountable and working in the best interests of the whole of Northern Ireland."
Politicians, public bodies and the business community have been reacting to the news that Northern Ireland Deputy First Minister Martin McGuinness has resigned in protest at the handling of a botched heating scheme that is likely to cost the taxpayer £490m.