It really depends on the airline, whether you are charged or not. It seems like some people still get their bikes on planes for free, but I would consider yourself very lucky if that happened. I checked Icelandair's website, and they charge $40 each way for the bike. I've seen it up to $100, so $40 is actually not so bad.

The best strategy for touring is usually to put the bike in a cardboard box you get from a bike store. Hardshell cases are very expensive, and they will not keep you from getting charged. Also you have to leave them somewhere once you get to your destination.