Six police officers died in pre-election violence, authorities reported.
Kenyans voted for the country's fourth president and other elected positions, including governors, senators and members of Parliament, Voice of America reported.
It was first presidential election since a disputed vote in 2007 that led to ethnic fighting in which more than 1,000 people died, Voice of America reported.
In advance of the latest voting, Kilifi County reported the police officers died in two attacks in Mombasa, which police blamed on the separatist Mombasa Republican Council.
Other acts of violence, including the torching of official Independent Electoral and Boundaries Commission vehicles and threats that caused several polling places to close, were reported.
"Very unfortunate, very regrettable, something that we condemn in the strongest terms possible, these heinous acts of aggression at a time when Kenyans are engaged in a very historic exercise," said Prime Minister Raila Odinga, a presidential candidate. "I am sure that our forces will apprehend those forces of darkness and bring them to book."
Presidential candidate Uhuru Kenyatta, who faces trial at the International Criminal Court on charges of helping to orchestrate the 2007 violence, said this year's election is about peace.
"Any issues that one may have, there is due process, there are the courts and everything else, which we should follow as opposed to inciting our supporters one way or the other," Kenyatta said. "Kenya will have a leader and that leader will be the leader of 40 million Kenyans ... ."
The big turnout and problems with electronic systems caused voting delays, officials said.
Peter Alingo of the Elections Observation Group said voting results would be sent from local counting centers to the national elections center in Nairobi on a mobile-phone system.
"So the next coming 24-48 hours are going to be very, very crucial, especially for Kenyans. Because that is where anxiety levels are likely to rise, and that is where tension is likely to be generated," he said.
Odinga and Kenyatta were virtually tied in recent public opinion polls. If no candidate wins the election in the first round, there will be a runoff vote in April.
Notable deaths of 2014 [PHOTOS]