I've heard people say they checked guitars at the gate, which saves some tossing, piling, and conveyor-belting. Hard shell cases are also recommended.

Re string loosening: it doesn't hurt to loosen the strings, but it can hurt to not loosen them. The first time I flew with my fiddle, I didn't know about this and wound up with three broken strings and a crack in the instrument. The problem may have something to do with temperature, but has a lot more to do with air pressure. Things that have air in them (such as wood cells) expand when the pressure drops if the air can't escape fast enough. The instrument gets bigger, the strings don't, and kablooie.