The 89-year-old Mugabe is Africa's oldest leader and is running for office for the seventh and perhaps final time.
His rival Morgan Tsvangirai hopes the election will usher in a new era for the troubled southern African nation.
Organisers reported high turnout across the country for the first election since the violent polls of 2008, that led to an uneasy power-sharing government between the two men.
There were no reports of widespread violence this time round, despite the fierce rhetoric of the campaign.
At many stations voters started queueing before sunrise in the winter cold hours before polls opened. The lines continued well into the evening, with many marking their ballots by candle light.
Mugabe voted before lunchtime in a Harare suburb, where he insisted the poll would reflect the will of the people.
"I am sure people will vote freely and fairly, there is no pressure being exerted on anyone," he said.
The one-time teacher came to prominence as a hero of Africa's liberation movement, guiding Zimbabwe to independence from Britain and white minority rule.
On Tuesday Mugabe vowed to step down if Tsvangirai was the victor. "If you lose you must surrender," he said.
Tsvangirai, the current prime minister, said that promise should be taken "with a pinch of salt".
Tsvangirai won the first round of voting in 2008, but was forced out of the race after 200 of his supporters were killed and thousands more injured in suspected state-backed attacks.
But the 61-year-old former union boss has repeatedly voiced concerns that the election is being rigged.
Finance Minister Tendai Biti, a senior member of Tsvangirai's Movement for Democratic Change, said the names of thousands of voters were missing from the electoral roll.
Biti, speaking after a meeting with the electoral commission, added: "They are admitting that there's still two million people who are dead on the voters' roll, but they said 'because they're dead, they can't vote'."
The MDC has handed its evidence to observers from the Southern African Development Community (SADC).
Since no Western groups were allowed to cover the presidential and parliamentary poll, the SADC's account will be closely watched.
In Washington, US State Department spokeswoman Marie Harf also said that early signs indicated a "peaceful environment" -- but that it was too soon to say if the election had been fair.
