I've flown all over the world with my bass. I've always taken my coffin case which is now so battered it's held together by gaffer tape and magic alone. Once, in Indonesia I saw my case coming along the conveyor belt with the side split and my bass half hanging out. That wasn't fun, but all was ok luckily. I swore then that I would never fly with that case again and would get a proper custom fit flight case, but due to the expense of them I haven't managed yet.
Normally I put my bass, pedals and leads in the case, wrapping a few T-shirts around things so they fit snuggly. I never lock my case as security have complained about this in the past, but I put one of those luggage straps around the case which stops it falling open if the catches get popped.
With more flying and touring on the cards next year I really do think that a proper flight case should be on my list, anyone know of any companies that offer endorsements/artist discount?
Thankfully I never have to take my amp-head.