The vote marks Pakistan's first transition from one civilian government to another in its 66-year history.
But sporadic violence linked to the election has claimed a number of lives. In the worst attack, 11 people were killed in a bombing on a political office in Karachi.
In the run-up to the election, more than 100 people died.
Tens of thousands of troops are deployed at polling stations after the Pakistani Taliban threatened to carry out suicide attacks.Hours before polls opened, Pakistan sealed its borders with Iran and Afghanistan in a bid to keep foreign militants at bay.
Officials said the borders would remain closed for the next three days.
Queues started forming before polling stations opened at 08:00 (03:00 GMT) on Saturday.
Abdul Sattar, 74, said: "We want change, we are really fed up with old faces coming back to power every time and doing nothing for the nation."
By midday, 30% of registered voters had turned out, election officials estimated, describing the figure as "very encouraging". An election commission spokesman said they hoped for a figure of 60-80% by the end of the day.
The turnout in 2008 was 44%.
While the streets of Islamabad were largely deserted, areas around polling stations were described as filled with crowds.
At a polling station on the outskirts of the capital, BBC World Affairs correspondent Mike Wooldridge said around 1,000 of the 4,000 registered voters had cast their ballots by midday, including a large proportion of women.
The BBC's Saba Eitizaz in Peshawar reported long queues of women, with many first-time voters excited about being part of the election.
EU observers in the eastern city of Lahore told the BBC that voting there was going smoothly and without any interruptions.
But voting was delayed at some polling stations in Karachi because ballot boxes and papers had not arrived. Electoral officials said staff had been threatened and attempts had been made to attack vehicles carrying ballot material.
Right-wing religious party Jamaat-e-Islami complained that some of its voters had been harassed and announced it was boycotting the vote in Karachi and areas of Hyderabad, reports said.
Polling stations will close at 17:00, however with an hour of voting remaining, there were still large crowds of voters and correspondents said it was likely that the polls would stay open for some time.
The Taliban on Friday warned voters to boycott polling stations in order to avoid attacks on the offices of political parties.
The militants have been blamed for numerous attacks throughout the campaign on Pakistan's three most prominent liberal parties.
The Pakistan People's Party (PPP) along with the Karachi-based Muttahida Quami Movement (MQM) and the Awami National Party (ANP) have been singled out for attacks by the Taliban.
As a result, the parties were forced to curtail their election campaigning.
Around two hours after polling started, a bomb attack was reported in Karachi, apparently targeting an ANP candidate outside the party's political office.
Eleven people were killed and more than 40 others were wounded, police told BBC News. The local ANP candidate, Amanullah Mahsud, who was in the office at the time of the attack, was wounded but not seriously.
The attack happened in the Landhi area of Karachi, an industrial district known for Taliban activity, the BBC's Shahzeb Jillani reports. Another ANP candidate and his son were shot dead close to the area last week.
Sporadic violence linked to the election was reported in several other areas of the country.
Seven people were hurt outside a polling station in the north-western city of Peshawar when a bomb went off attached to a motorcycle
A suicide bomber blew himself up after police prevented him from entering another polling station in Peshawar, police told AFP
A clash between two groups at a polling station in Chaman on the border with Afghanistan left least three people dead and several others hurt
An explosion was also reported in Quetta in the south-west
At least four people were hurt in a blast in Mardan in the north-west
Militants have so far avoided targeting the campaigns of Pakistan Muslim League-Nawaz (PML-N) of Nawaz Sharif and the Tehreek-e-Insaf (Movement for Justice) party of Imran Khan, who is recovering in hospital after a fall at a party rally.
Mr Sharif, who was deposed as prime minister in a military coup 14 years ago, is seen as favourite to return for a third term of office.
As he voted in Lahore, the former PM said he was hopeful of victory.
In a bid to clamp down on corruption, election officials said electoral rolls had been refreshed and a text messaging service would provide voting information.
However, the Human Rights Commission of Pakistan on Friday expressed "acute concern" about the manner in which the violence has "impaired the fairness of the elections almost beyond repair".
It called on all institutions to "stretch themselves to their absolute limit to ensure security of voters, candidates and polling stations on Saturday so that the people can exercise their right to choose their representatives".
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