I do disagree though that deporting is the way to go. The problem is real, and shoving it under the carpet doesn't really solve much of it. What is needed is an EU-wide solution, and it needs to be well-thought and well implemented, because the problem isn't easier.
We've had a lot of negative feedback here in Romania because of the various criminals we exported to Italy. To my surprise when I went to visit Rome I found surprisingly large, very prosper and very hard-working Romanian minority. Yes, we exported beggars and criminals, but the number of "legitimate" immigrants was dwarfing them.
This is the main purpose of an open EU - to move labor, capital and markets where they are naturally needed. I'm pretty sure even northern countries like Germany, France or Holland (and quite possibly even Sweden) benefit from highly trained immigrants from Eastern Europe. I personally know Romanian doctors who lives in each of those countries. Sadly, Romania can't afford to retain good doctors - but this is how an open market works.