It is the first time a vote has taken place under a new constitution, designed to prevent a repeat of violence that followed the 2007 polls.
More than 1,000 people died when supporters of rival candidates clashed over a contested result.
Despite appeals for calm, reports say at least four police officers died in clashes near Mombasa early on Monday.
Officials said a gang attacked police in the region of Changamwe outside the port city in the early hours.
Eyes on the presidency
Kenyans will choose a president, members of parliament and senators, county governors and members of the newly-formed county assembly.
However, the BBC‘s Gabriel Gatehouse in the capital Nairobi says all eyes are on the presidency.
Eight candidates are standing but it is essentially a two-horse race pitting Prime Minister Raila Odinga against Deputy Prime Minister Uhuru Kenyatta, he says.
Mr Kenyatta, son of Kenya’s founding father Jomo Kenyatta, is due to stand trial at the International Criminal Court for his alleged role in orchestrating the violence five years ago.
Mr Kenyatta’s running mate, William Ruto, has also been indicted by the court. Both men deny any wrongdoing.
The post-election violence of 2007-8 broke out after Mr Odinga claimed he had been cheated of victory by supporters of President Kibaki.
Supporters of the rival candidates, from different ethnic groups, took up arms against each other.
Mr Odinga later joined a government of national unity under a peace deal.
Our correspondent says long queues formed outside polling stations in Nairobi hours before polls opened.
The atmosphere was calm, he said, and people chanted “peace”.
‘Keep the peace’
In the run-up to Monday’s vote, President Mwai Kibaki – who is not seeking re-election – urged Kenyans to vote peacefully and for the losers to accept defeat.
“Cast your vote and keep the peace,” he said in a televised address to the nation on Friday.
“Let us send a clear message to the world that our democracy has come of age. A peaceful vote is a vote for a secure, prosperous and stable Kenya.”
Candidates have also promised to respect the result and urged their supporters to refrain from violence.
Clerics across Kenya also gave sermons dedicated to peace on Sunday.
The police, however, have warned of conspiracies to cause chaos – in Nairobi and elsewhere – and have made it clear that violence will not be tolerated.
Security is being stepped up with some 99,000 police officers being deployed around the country, at polling stations and vote-counting centres.
The polling stations are open from 06:00 to 17:00 local time (03:00-14:00 GMT).
Presidential candidates must secure support from across the country to be declared the winner, so they cannot just rely on support from their ethnic groups, as has been the case in previous elections.
Official results will be announced by 11 March by the electoral commission.
If no candidate obtains more than 50% of the vote there will be a run-off, probably on 11 April.