Lufthansa are, from what I've heard, the best airline to use if you're flying with an instrument. They're usually pretty good for letting you take them on board, but despite it now being EU and US law that they have to let you take your instrument on board the plane, it's still a total crapshoot as to whether or not you'll actually get to. My advice would be to get a good, solid gigbag - something like a Protection Racket case (Product Display
), and pack the guitar inside it really well - fill the case with towels and t-shirts and anything soft that you're taking with you. That'll stop the guitar moving in the case and it'll protect it against being thrown about - that's what I've done when I've flown with guitars before, and it's never been a problem.
The Protection Racket cases are really good btw. They're made of high density foam and they're tough as all hell. I threw my guitar in one of those cases down solid stone stairs once (don't ask), and there wasn't a mark on anything - not the guitar, not the case, not a thing. They're pretty reasonably priced as well.