Mwai Kibaki, the incumbent president, is vying for the top job with former ally Raila Odinga, who is determined to realise a long-held dream of leading the region's top economy.
In Nairobi's vast Kibera slum, gunmen shot dead one man and wounded two others near a polling station.
Voting had been due to stop at 5:00 pm (1400 GMT) nationwide but was extended in many regions after some polling stations opened late due to heavy rains and delays in the arrival of polling staff and equipment.
"Those polling stations that opened on time have closed and those where voting started late are going on," Jack Tumwa, an official with the electoral commission, said.
Official and definitive results are only expected on Friday but partial results could start filtering as early as Thursday night.
Alexander Graf Lambsdorff, the chief EU election observer, said he had seen no evidence of fraud.
Voters were choosing their president as well as 210 members of parliament and some 2,000 local councillors.
Opinion polls in the run up to the elections suggested that the contest would be very tight, with Kibaki and Odinga in a neck-and-neck race.
If Kibaki loses, he will be Kenya's first sitting president ousted at the ballot box. Analysts say the chance of a second transfer of power in two elections shows democratic maturity. Others fear it heightens the potential for trouble.