I've flown with my guitars a handful of times...
The first time around 2003[?], for an important audition, I purchased a seat for it, no problems there... If you have an expensive instrument, crummy case, or are otherwise afraid something might happen, this is the safest way to go. All it takes is a short drop onto the concrete by a baggage handler and your instrument is gone.
Now, if possible, you could always airmail [fedex, etc] your instrument overnight to the location you need to get it to. That round-trip will most likely cost you less than a seat, and the airmail's insurance policies are better than the airlines [last I read airline instrument policy would only pay up to $2500]
If you fly a lot, another option is to buy the strongest, lightest, most form-fitting case you can and still hope you don't have to check it. Something like an Accord case. I like to carry my guitar upside-down with backpack straps, so that the neck points to the ground rather than the sky. This will eliminate lots of issues with checking in, boarding and/or gate-checking your instrument.
Then when boarding, ask the crew to put it in the crew's closet [it's usually near the door as you walk onto the plane]. If they're nice, they'll let you put it in... if not, you'd have to try for an overhead compartment and a few nice people that will put their belongings at you feet.
The key is to be nice to everyone--staff, security people, airplane crew, other passengers-- it goes a long way.