In 2009, only 43 percent of all eligible voters in the then 27-nation EU turned out to vote – and in many of the individual countries the voter turnout was low, or high in countries, such as Belgium, where voting is compulsory.
Alastair Newton, senior political analyst at Nomura, told CNBC that investors who didn't think that EP elections were important were "wrong about that," adding that if a large number of nationalist parties were able to form a formal alliance, Europe could face "significant additional difficulties."
"Extensive wins for euroskeptic parties (i.e. around 30 percent of the seats according to some opinion polls) are likely to act as a drag on investor sentiment," he told CNBC.
Futhermore, Newton warned, "a strong showing by such parties will pull mainstream parties in government (and opposition, for that matter) into more euro-skeptic stances, "which is also likely to act as a drag on long-term stabilization – and, in many case I suspect, on pushing through structural reforms urgently needed to boost competitiveness and growth."
Unfortunately for European officials, the latter fundamentals are just what the region needs but as yet, there is no end to the euro zone crisis in sight. While euro zone unemployment is stuck at a record high of 12.1 percent, economic growth is near flat in both the EU and euro zone.
(Read more: Euro zone jobless at record high as retail sales surge)
As such, the vicious circle of little or no growth and increasing voter disillusionment could push more people into the arms of extremist parties. With names like "Freedom Party of Austria" or "For Fatherland and Freedom" in Latvia, far-right wing parties in Europe nail their colors firmly to the mast in terms of nationalist agenda.
Despite their controversial character, such parties have seen strong gains in national elections. For instance, Austria's Freedom Party gained 21.4 percent of the vote in national elections last year, not far behind the winning social democrats and conservative party.
"An economic recovery in the EU or debt relief in the euro zone would probably help [dispel the rise of these parties but] as neither are very likely, I expect we are in for a tough period for the EU," politics professor Rob Ford from the University of Manchester, told CNBC.
If such parties do as well as they are expected to in the elections, he added, the next European Parliament could prove to be "a very volatile and unpredictable institution."
"Governing Europe is already hard; it is about to get a lot harder," Ford added.
- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt.