While voting was generally reported to run smoothly and without disturbance, there were some complaints of irregularities and minor violence.
The opposition accuses Mugabe of plotting to steal the election.
Tensions rose on Friday, with soldiers and police in a convoy of armored personnel carriers and water cannon patrolling through downtown Harare, the capital, and the security chiefs warning against violence.
Police presence at the polls was heavy on Saturday.
Running against Mugabe are opposition leader Morgan Tsvangirai, 55, who narrowly lost the disputed 2002 elections, and former ruling party loyalist and finance minister Simba Makoni, 58.
Makoni threatens to take votes from both the opposition and the ruling party.
All three candidates voted early on Saturday, with Mugabe telling reporters he would accept whatever results emerged and rejected opposition charges he had already orchestrated his own victory.
Independent monitoring watchdogs have complained there were too few stations in urban opposition strongholds, and that they have seen the names of dead or fictitious people on the official voting list.
Speaking to AP Television, Tendai Biti, Secretary General of Tsvangirai's Movement for Democratic Change, said that there had "been a number of blatant breaches of the law".
"For instance, the fact that our election agents are not being allowed inside polling stations," Biti said.
He said that "in some polling stations there were no ballot papers".
On Friday night, monitors from the 14-nation Southern African Development Community said they had observed "a number of matters of concern," which they did not identify.
Zimbabwe has barred observers traveling from the United States and the European Union, but the U.S. State Department said it had 10 people from its embassy in Harare monitoring the elections.
The economic collapse of what was once the region's breadbasket has been a central campaign issue, with the opposition accusing Mugabe of misrule and dictatorship.
Mugabe, appealing to national pride, blames the West, and claims his opponents are stooges of former colonial ruler Britain.
Zimbabweans are voting in a single day for the first time for president, 210 legislators, 60 senators and 1,600 local councilors.
There are 9,000 polling stations for 5.9 million voters.
"I don't think there's anyone who's going to get more than 50 percent, probably we are going into a run-off," one Harare resident told AP Television.
"I'm indifferent. I don't feel I can vote for anyone. There's no presidential candidate for me," another man said.
Preliminary results are expected by Monday.
In the southern African country that once exported food, tobacco and minerals, Zimbabweans struggle to survive inflation in excess of 100,000 percent, crippling shortages of food, water, electricity, fuel and medicine.
A third of Zimbabwe's population, an estimated five million people, are political and economic refugees.