Polling stations opened at 04:00 GMT on Sunday to allow around 9.8 million voters to cast their ballots.
The first exit polls are expected immediately after voting stations close at 1600 GMT.
Most Greeks welcomed Karamanlis's call for early elections last month, hoping that a new administration will halt the economy's slide.
It is not clear, however, whether the Socialists would win an absolute majority in 300-seat parliament and end up governing alone.
Under Greece's electoral laws, the winner needs 42.5 per cent of the vote for an absolute majority. If Papandreou fails, another election will be needed.
Greece's conservatives won 41.8 per cent of the vote and 152 seats in parliamentary elections in September 2007.
Pasok garnered 38.1 per cent of the vote and 102 seats.
Parties expected to pass the three per cent hurdle to enter parliament, include the Communist Pary of Greece KKE, the Coalition of the Radical Left (Syriza) and the ultra-conservative People's Orthodox Alarm (Laos).
Barnaby Phillips, Al Jazeera's correspondent in Athens, said that if there was not a clear winner in the elections, it would "be very bad news for Greece" because of the country's current social and economic problems.
"You would have a caretaker-minority government and the very real possibility of another election, as soon as November," he said.
"I think that is something that Greeks of all political persuasions do not want. There is a consensus that the last thing Greece needs, along with all the economic and social gloom, is a prolonged period of political uncertainty.
"But it is a possibility, unfortunately."