The turnout for the election was 63.84%, compared to 68.8% in the 1998 Assembly election.
A power-sharing executive will not be re-established at Stormont immediately after the election.
A review of the workings of the Good Friday Agreement and a further round of negotiations is expected to begin after the election.
BBC Northern Ireland's political editor Mark Devenport said there were clear swings from the Ulster Unionists to the DUP with the DUP mopping up many small independent unionist groups.
He also said there was very strong showing by Sinn Fein as the dominant nationalist party.
Speaking after his election, Mr Trimble said the focus remained on republicans.
"My ultimate aim is to see a society here operating entirely peacefully and democratically and so, the first object now, as it was beforehand, is the matter of compelling republicans that they have to now abandon all elements of their military machine."
Mr Durkan welcomed his election but said he was worried about the future of the Agreement.
"I'm worried, not so much for the SDLP or whatever, I'm just worried about what this result means for our political process, what it means for the future of the Agreement."
Mr Paisley said it was "a good day for the DUP".
"We are going to have a proper negotiation for a new agreement that will enable the democrats, and the democrats only, to buy into something that is stable," he said.
Speaking after his election in west Belfast, Sinn Fein's Gerry Adams said people had endorsed his party's republican vision.
The final results are not expected until Friday
"We asked people to endorse the risks we were taking for the peace process, we stood on our record in the assembly and the executive," he said.
In Lagan Valley, the anti-Agreement Ulster Unionist candidate, Jeffrey Donaldson, topped the poll with just over 14,000 first preference votes.
"The unionist electorate are very unhappy with the Agreement," he said.
In South Antrim, the anti-Agreement Ulster Unionist candidate David Burnside was also elected on the first count.
In Mid-Ulster, the DUP's William McCrea topped the poll, with only 22 votes to spare over Sinn Fein's chief negotiator Martin McGuinness, who was also elected on the first count.
The DUP's Gregory Campbell has been re-elected in East Londonderry where he topped the poll.
DUP candidates Nigel Dodds and Peter Robinson of the Democratic Unionist Party topped the poll in North and East Belfast respectively.
Iris Robinson of the DUP was elected on the first count in Strangford, where she topped the poll. Lord Kilcooney (John Taylor) of the Ulster Unionist Party was also elected on the first count.
Votes are being counted on Thursday, with a final result expected to emerge early on Friday evening, barring recounts.
Ulster Unionist leader David Trimble said he was confident the party would remain the largest unionist grouping after votes were counted.
The last assembly election in 1998 returned 28 Ulster Unionists, 24 SDLP, 20 DUP and 18 Sinn Fein MLAs.