The poll in the vast, energy-rich North African country is expected to be the freest since independence from France in 1962 and signals Algeria's return to the international fold.
From Mediterranean shores to the Sahara desert, some 40,000 polling stations opened at 8am (0700 GMT) and were scheduled to close 12 hours later. There were 18 million eligible voters in the country of 32 million.
Opposition candidates have cried foul and accused authorities of planning fraud but offered no evidence to back the allegation.
President Abd al-Aziz Boutaflika is the favourite of six candidates to win an unprecedented second mandate until 2009. His main challenger was Ali Benflis, 59, his campaign manager in 1999 and prime minister until he sacked him a year ago.
Other candidates included an Islamic leader, a Trotskyite woman - the first female presidential candidate in the country - and a champion of the Kabylie region, home to a restive ethnic Berber minority.
Boutaflika, 67, is credited with all but ending a jihad which flared after the military prevented an Islamic party from gaining power at the ballot box 12 years ago.
"The military's total withdrawal from the political scene has always been a pre-condition for democracy to take root"
communication and culture minister, Algeria
At least 100,000 people were killed in the decade of conflict since then, the government says. Human rights groups say 150,000.
Boutaflika was elected with nearly 74% of the vote in 1999 after all other candidates withdrew on the eve of election day, charging that the polls were rigged.
Allegations of fraud have marred all elections in Algeria since multi-party politics took root 15 years ago, with the powerful and opaque military establishment acting as kingmaker.
The army has pledged neutrality this time, an unprecedented statement of confidence in the country's fledgling democratic credentials. Apart from Boutaflika and with the exception of Algeria's first head of state in the early 1960s, Ahmad Bin
Billa, all presidents have been former generals.
"The military's total withdrawal from the political scene has always been a pre-condition for democracy to take root," in Algeria, said Communication and Culture Minister Khalida Tumi. "It was not possible during this past decade of bloodshed."
If no candidate wins more than 50% of the vote, the election will go to a second round run-off between the two leading candidates on 22 April. Official results are not expected until Friday.