I'm writing this from Chicago Midway. While I'm not on my way to Europe, thought I'd relate that I was not charged a cent on Southwest Airlines today. They are by far the best in my experience and their charges for basses are usually $50 and it's never a hassle.
My experience going to Europe a few times a year have been similar to Mr. Arnopol's. Sometimes there's no charge. The most I was charged was $375 one way on KLM to Copenhagen. Oddly enough on the return flight on that trip I wasn't charged anything. Same airline, same connection. It really just comes down to the ticket agent.
Some airlines have a stated "no bass" policy such as US Airways, but for the most part they'll take it. If they'll take surfboards, then they'll take a bass. I couldn't agree more about not calling the airline. In my experience that only results in a big fat "No" for an answer. Like I said, I use a lightweight hard foam case which is still oversized but not overweight.
I used to use a Stevenson Trunk, which was massive and heavy, and had fine luck with that too but I was always charged and it really was a lot more trouble to handle. The foam case with a plywood bass is really easy for one person to manage and because it's so light it slips by without a charge more often.
I've also just heard of this new design:
http://foldingbass.com/
It looks cool, especially if it could be done as a retrofit. Too bad there aren't any pictures of the case on the website.
Good luck!
Corey