Guitars on a plane are as bad as "Snakes on a plane" in my opinion. However, if you have a good sturdy ATA case, there's usually no need to worry. If you DON'T and your guitar ends up in the cargo bay...be afraid....be VERY afraid.
I've lived and learned with this over the years. Thankfully none of my guitars were ever damaged, but some of my cases were which is what made me change up my gameplan. If you can't afford a killer ATA case, there are other things you can do that work wonders.
First off, and this is a must even if you have an ATA case. Wrap the important parts of the guitar in bubble wrap. If you can buy enough to where you wrap the entire guitar, do it. But if not, wrap anything that can move. For example, those that use floating trems like a Floyd etc or any trem at all, put a piece of bubble wrap under the trem so that the trem doens't slam into the wood of the guitar. Bubble wrap under the back of the neck where the guitar lays in the case and a sheet on top of the guitar. This can really help and is easy and affordable.
Next, I always like to bring two guitars with me. In this example, two ATA cases would be a bit pricey. So I'll use two regular cases, do the bubble wrap thing and then put both guitars into a hockey bag. This counts as one item. Slap fragile in as many spots as you can on the bag and the cases. Not that it matters, but it looks cool.
In all my years of flying all over the world, I've only seen one guy treat my instruments like a human being. An elderly gent from Continental (who I always seemed to get handling me when flying to Europe) was so gentle, it was awesome. I find out he was a guitar player...so it's understandable why now. :)
Tuning: I've heard mixed reviews on this that you should lessen the tension on your strings when flying. I tune down to a low C by default, but I never touched my tuning. Coming fresh off a plane, my guitars are usually in near perfect tune other than my low E (which is a C for me) being a few increments sharp or flat.
+1 to Tim's advice on opening the case. Definitely try to wait for as long as you can. That said, you should open it immediately just to quickly check to see if your guitar is ok. Just dont spend any great length playing it or examining it for little details. See that it's there, nothing is broken and close it back up for an hour or two. You'll notice the guitar will be freezing cold...this is why you want it to stay in the case closed up for a while as the sudden temp change could really effect it. Then again, most of us are in situations like this all the time with our guitars if you play live. I've done shows in the freezing cold where my guitars were kept at room temp before I played only to be frozen when I played live. I've kept them in 72 degree air condition and then played in 105-120 degree heat....it can definitely take a toll, but that goes with the territory when you play live.
-Danny