The main contenders, the left-wing Syriza and right-wing New Democracy, are at odds over whether broadly to stick with the tough EU bailout deal, or reject it and boost social spending.
EU leaders say that to reject it would lead Greece out of the eurozone.
The poll, the second in six weeks, was called after a vote on 6 May proved inconclusive.
Sunday's vote is being watched around the world, amid fears that a Greek exit from the euro could spread contagion to other eurozone members and send turmoil throughout the global economy.
Tough austerity measures were attached to the two international bailouts awarded to Greece, an initial package worth 110bn euros (£89bn; $138bn) in 2010, then a follow-up last year worth 130bn euros.
Many Greeks are unhappy with the conditions attached to deals which have been keeping Greece from bankruptcy and all but one of the parties standing for election have promised some degree of renegotiation of the terms.
In remarks quoted by the Reuters news agency a few hours before polls opened, the head of the Organisation for Economic Co-operation and Development Angel Gurria suggested that the next Greek government should be given a chance to revisit the bailout conditions.
"If that is the condition presented for Greece to stay [in the eurozone] and then move on, I would say it is probably something that should be attempted," he was quoted as saying.
But Germany, which has the eurozone's most powerful economy, insists Greece, like other member-states which have received international bailouts, must abide by the austerity conditions.
On the eve of the vote, Chancellor Angela Merkel said: "It is extremely important that tomorrow's Greek elections lead to a result in which those who form the government say, 'Yes, we want to keep to our commitments.'"
Like Mr Gurria, the German chancellor and several other European leaders will be attending the G20 summit in the Mexican resort of Los Cabos on Monday, which is set to be dominated by the eurozone crisis and the aftermath of the election.
The head of New Democracy, Antonis Samaras, told supporters on Friday that he would lead the country out of the financial crisis, while staying in the eurozone.
He broadly accepts Greece's international bailout, but says he will renegotiate the terms of the agreement to seek a better deal for Greeks.
"We will exit the crisis; we will not exit the euro. We will not let anyone take us out of Europe," Mr Samaras said.
The youthful head of Syriza, Alexis Tsipras, rejects the bailout, but wants Greece to stay in the eurozone, saying a bailout is possible without the kind of drastic cuts demanded of Greece.
"Brussels expect us, we are coming on Monday to negotiate over people's rights, to cancel the bailout," he told a final rally on Thursday.
By BBC News, June 17, 2012