The first week of June should see 500 million EU citizens exercise their right to vote for Members of the European Parliament (MEPs). The EU does not have a single electoral law for these elections. Many details are decided at a national level, but a basic set of rules has been established in 1999: MEPs must be elected on the basis of proportional representation, the threshold must not exceed 5%, and the electoral area may be subdivided in constituencies if this will not generally affect the proportional nature of the voting system.
Apart from these common principles, Member States are free to choose their voting system: consequently, some use Mixed Member Proportional Systems, Malta and Ireland favor the choice voting (or "the single transferable vote) and most use list-PR, whether at a national level or in regional constituencies, with open or closed lists, with high or low threshold. The wide range of proportional systems used for European Parliament elections is a perfect illustration of the almost infinite number of proportional voting systems possible.
No wonder why PR has been chosen as the least common denominator and basic rule between the various electoral systems. Indeed, PR is widely used in the EU (24 out of 27 Member States currently use PR to elect their Parliament). In the few countries with a winner-take-all political culture- notably France, and the UK- the contrast between often unrepresentative national politics and more healthy, diverse and competitive European elections is sticking.
As an example, the British Green Party has never earned any seat at Westminster. Back before 1999, when the UK used first-past-the-post to elect its European Member of Parliament, the Green Party had excellent electoral results (15% one year) that did not earn any MEP seats -- indeed, winner-take-all prevents parties with large but geographically spread out vote shares from receiving any seats. Since proportional voting was adopted for European elections in the UK (within regional constituencies), the Green Party has been fairly represented in proportion to its share of votes: with about 6% of the votes in both 1999 and 2004 elections, it won 2 of the 79 British seats in the European Parliament.
Another notable effect of PR for European Parliament elections is the better representation of women. Women are better represented in the EP than in nearly all national assemblies in Europe. The discrepancy between women elected at the European Parliament and in the national parliament is really significant in countries that use winner-take-all at a national level. As an example, 42.3% of the French MEPs are women, as opposed to 18.5% of national MPs. Similarly, 26% of the British MEPs are women, as opposed 19.8% of national MPs (more data here)
The European Parliament is widely considered the most legitimate institution in the EU today. Its influence over the European decision-making process and inside the EU "institutional triangle" is steadily growing. Its members are reputed good, representative and responsive lawmakers. There is little doubt that the PR feature of the EP elections plays a major role in this growing confidence and influence.