I read yesterday (sorry, I can't remember where) that most of this phenomenon is caused by apathy of the average European citizen. The voter turnout for the Euro elections is really low, giving way to fanatics to take office, just because they're the ones making the most noise. Even so, the real amount of far-right members of the European Parliament is really low.
You're right about the apathic feelings that a certain number of EU citizens have towards the EU. Those feelings include several topics, such as sovereignty of the individual member states, open borders and immigration, and corruption. Simply put, many people desperately want reform. In the past, however, prominent people within the EU named these eurosceptic feelings populistic. With these new results, the EU will hopefully learn to understand what caused these eurosceptic feelings to come into existence. Besides that, almost 1 in 5 seats in the EP will go to Eurosceptic parties, which is not exactly 'really low'. Edit: I also think that so-called 'anti-democratic' parties fit perfectly within the European Parliament. Do the referendums of 2005 ring a bell?