I just had to go through this when I flew down to Mexico to play. I checked my bass and my guitarist checked his guitar. Both in hard shell cases. I wouldn't dare check a soft case. Everything came back great. Not a whole lot can happen if your guitar is tucked away in a hard shell case with good padding. They even make cases specifically to travel with on planes so if you are willing to drop some money for a new case that's an option.

Don't lock the case because TSA will most likely unlock it and check it.

Also, if it is a REALLY expensive guitar that you absolutely don't trust to check, some airlines let you purchase another seat just for your guitar. More expensive obviously, but less expensive than a broken $10,000+ guitar.