The elections, which are spread over four days in the EU's 28 member states, are expected to see major gains for parties bent on dismantling the European Union from the inside.
The vote comes as the EU struggles for relevance in the aftermath of the euro financial crisis and as it grips with the chaos in on its borders in Ukraine.
"I believe in Europe, but I think there are far too many rules coming from Brussels," Margreet de Jonge, 63, told AFP as she cast her ballot in The Hague, echoing the view of many that the EU has become a bloated bureaucracy.
When the results are announced from 2100 GMT on Sunday, eurosceptic parties may top the polls in Britain, France, Italy and the Netherlands.
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The anti-immigration and anti-EU UK Independence Party (UKIP) of Nigel Farage, and Geert Wilders' virulently anti-Islam Party of Freedom (PVV), are both forecast to make big gains.
UKIP's rise has rocked the British political establishment as a party without a single representative in its national parliament heads into the European election ahead of the main opposition Labour Party, according to polls published by the Times and the Daily Mail newspapers on the morning of the vote.
The European parliament has largely been dismissed as toothless in the past, but these elections are different because the winning bloc will for the first time be able to nominate a replacement for outgoing European Commission President Jose Manuel Barroso.