I entered the European Union (actually the Schengen zone, which is kind of the same as the E.U. but slightly different) in Iceland, and thought that I could now stay for a couple of months since I'd been gone for more than two months. I was somewhat winging it based on several different articles I'd read about how it worked (note: I don't recommend winging it when it comes to possibly overstaying your time in foreign countries!). But they let me in at Iceland, so all seemed well at that point.
Then a week ago, as I was considering my upcoming travel plans, I realized I should get a little more specific and figure out exactly how much longer I was allowed. And I eventually figured out that, whoops, I was pretty sure I'd overstayed my time by about two weeks already at that point, because I hadn't stayed out of the E.U. long enough before re-entering. I looked around online for what the potential consequences were for overstaying in the Schengen zone. But there's no specific punishment. However I did come across someone who had been fined 700 euros for overstaying by a few weeks.