Aung San Suu Kyi’s National League for Democracy (NLD) is expected to win the most parliamentary seats, although she is barred from the presidency.
The ruling Union Solidarity Development Party (USDP), backed by the military, has been in power since 2011.
Large crowds gathered in Yangon as Ms Suu Kyi arrived to cast her vote.
Wearing her trademark thazin flowers in her hair, she smiled and waved, but left without comment.
Across the country, long queues formed at some polling booths, with reports of people waiting from before dawn.
“When I cast my vote I was very excited and so worried that I might do something wrong that my hands were shaking,” said Kay Khine Soe, in Ms Suu Kyi’s Kawhmu constituency.
Voting in Yangon, Wuhan Datong said: “I am 57 years old. I never participated in the previous voting since I had doubts over it. But the election this time is fair. So I have come to vote.”
About 30 million people are eligible to vote in the election in Myanmar, also known as Burma. Clear results are not expected until Monday morning.
More than 6,000 candidates from over 90 parties are vying to be elected to the 664-seat parliament in the first national elections since a nominally civilian government took power in 2011.
However, 25% of seats are reserved for unelected military representatives, who are expected to side with the USDP.
Ms Suu Kyi, a former Nobel Peace Prize laureate, is barred from the presidency as the constitution disqualifies anyone with foreign offspring – her children are British.
The NLD must take 67% of all contested seats in order to gain a majority.
On Thursday, she said she would be “above the president” if her party won.
Current President Thein Sein said he would accept the election result. He cast his ballot at a school in the capital, Naypyidaw, built in 2005 by the military.
I watched people lining up in the dark long before the polling station opened in the Kyi Myin Daing neighbourhood, which straddles the Yangon River.
As the sky brightened, the queue stretched to the end of this crowded street and around the corner. There were people of all ages: young women in jeans and T-shirts, older men and women in more traditional Burmese longyis, all clutching their pink national identity cards and white voter registration documents.
The one thing nearly all of them have in common is that they have never before had the opportunity to elect a new government.
There have been reports of irregularities, intimidation and people being left off official voter lists, but, at this polling station, we saw no problems, with officials calmly explaining the procedure for filling out ballot papers and placing them in the sealed boxes.
Here voting took place in a temporary marquee erected between run-down old apartment blocks. Several young men helped lift an older man in his wheelchair inside to vote.
Everyone we spoke to expressed their happiness about this historic moment, and their hope that it would help make theirs a better country.