But scores of voters in south-western Uganda, the home of President Museveni's chief rival Dr Kizza Besigye, said they were denied the right to vote, claiming that supporters of Mr Museveni had stuffed the ballot boxes.
Turnout was high at polling stations and final results are not expected before Tuesday, though the Electoral Commission has until Wednesday afternoon to report them.
Contrary to local fears the day appears to have gone off smoothly, with no incidents of major violence being reported.
But scores of voters in south-western Uganda, the home of President Museveni's chief rival Dr Kizza Besigye, said they were denied the right to vote, claiming that supporters of Mr Museveni had stuffed the ballot boxes.
"They have put my ballot in the ballot box, even though I did not vote," Patience Tumuwijukye, 29, complained.
Vote rigging denied
The chairman of Katete town council, Marias Rugesira, denied the accusations, even as town residents shouted over his shoulder, calling him a liar.
Mr Museveni is running against five challengers for a second and final five-year term as president. He must win more than 50% of the vote to avoid a runoff.
Many voting stations stayed open past the official closing time to accommodate voters still in line.
Where the polls had closed, people crowded around to watch each vote counted by hand and to hear the local results.
Voters intrigued
The atmosphere on election day was full of anticipation.
Ugandans are intrigued that the man who has emerged to challenge Mr Museveni is an old friend.
Mr Museveni says that he needs another five years in office to carry on the process of stabilisation and modernisation, which he has begun.
But 44-year-old Dr Besigye, who served as Mr Museveni's doctor during the five-year bush war, has accused Mr Museveni of presiding over an administration full of corruption and nepotism
He has struck a chord with people who feel that their own lives have not improved.
Mr Museveni has also been criticised for banning political parties, which he has blamed for fomenting ethnic and sectarian hatred.
Still revered
Nonetheless Mr Museveni has consistently led in opinion polls.
He is still revered by many Ugandans for leading a guerrilla campaign, which brought relative peace and an end to a period of brutal dictatorships in 1986.
He has also been praised in the West for his economic reforms.
Independent election monitors are appealing to supporters of both camps to accept the election result gracefully.