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Last election 334,558 advance votes were cast, or 14.7 per cent of total votes, and an increase of 3 per cent from 2008.
Special votes are also open from tomorrow - a special vote is one that is cast from outside your electorate.
Mr Cunliffe, the Labour leader, is standing in New Lynn, so will cast a special vote in Christchurch this morning.
"Because I want all people to know that they can vote from today - they don't need a special reason - I will be encouraging all New Zealanders to vote early so they know they've done their part in bringing a positive future to New Zealand."
National leader John Key will vote on election day.
Many organisations are promoting advance voting, including the Human Rights Commission and the Internet-Mana Party.
Internet Party founder Kim Dotcom will vote in Auckland this afternoon, where he will also launch Internet-Mana's Mobilize campaign, a tool to get people to commit to voting.
Mr Dotcom can vote as a New Zealand resident, but he cannot stand for Parliament because he is not a citizen.
People can pledge to vote through Mobilize, and receive a unique pledge code via text message, which they then share with friends, family and colleagues though social media and email.
Officially, anyone can vote in advance if they are not going to be in their electorate or cannot get to a voting booth on election day. But in practice anyone can vote in advance because a reason no longer has to be provided.
Advanced and special voting
• Opens from today
• Anyone can do it
• Over 300 voting places countrywide
• 334,558 advanced votes cast in 2011, 14.7 per cent of total vote
www.elections.org.nz/events/2014-general-election/information-voters-who-when-and-where