Security was tight as polls opened at 7:00 am (0230 GMT) after the Islamists rejected the election as a foreign plot and urged their fighters to attack polling staff, voters and security forces.
Afghanistan's third presidential election brings an end to 13 years of rule by Karzai, who has held power since the Taliban were ousted in 2001, and will be the first democratic handover of power in the country's turbulent history.
Interior Minister Omar Daudzai said all 400,000 of Afghanistan's police, army and intelligence services were being deployed to ensure security around the country.
But there were no major incidents in the first two hours of polling today and preliminary observations suggested stronger turnout than in 2009, when only around a third of eligible voters cast their ballots.
In Kabul, hundreds of people waited in cold wet weather to vote amid stringent security, despite the insurgents' promise of violence.
Around 13.5 million people are eligible to vote from an estimated total population of 28 million, with polls due to close at 4:00 pm.
Karzai, who is constitutionally barred from standing again, voted for his successor in a school near the presidential palace in Kabul.
"I urge the Afghan nation to go to the polling stations despite the rain, cold weather and enemy threats... And to take the country another step towards success," he said.
As well as the first round of the presidential election, voters will also cast ballots for provincial councils.
All three voted soon after polls opened.
There is no clear favourite and if no candidate wins more than 50 per cent of the vote in the first round - preliminary results for which will be announced on April 24 - a run-off is scheduled for late May.
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