When I travel with my DJI Phantom, I usually use a Nanuk 940 case with pick ‘n pluck foam. It comes full of foam cubes that are partly stuck together, and you just rip out cubes to make space for whatever you want to put in the case. The Nanuk fits into overhead bin space in most airplanes, and also fits in that carry-on tester you see at airport gates. I like the Nanuk case better than the Go Professional case that a lot of people buy because I could configure it more efficiently, and can fit a full FPV setup in there with both monitor and goggles.
I’ve also lashed my Phantom to the outside of a backpack, which works pretty well for hiking, but leaves the Phantom and gimbal exposed to the elements.
Today, I tried something different. I packed a Phantom into a Think Tank Airport Acceleration backpack (the current version is the Airport Accelerator Backpack), which is the pack I normally use when I travel for underwater photography. The entire insides of the backpack can be removed and reconfigured, which makes it perfect for holding large things like quadcopters. I configured the large divider panels so they hug the contours of the Phantom, giving me plenty of space to put in the radio, which has a Black Pearl diversity receiver monitor attached to it via a Rave Aerial Video 3D-printed monitor mount (the best one, in my opinion). I also can fit a bunch of extra batteries (or two Phantom 2 battery chargers, as shown in the pictures), and a bunch of other accessories. The separate computer bag (integrated, in the new version of the backpack) can be used to hold a computer and/or iPad, etc.
The backpack is pretty bulky, but it is a lot easier to carry around than a hard case!
I know of a couple dedicated Phantom backpacks being developed right now by third parties, so it looks like there will be some off-the-shelf options soon.
Update: The Vanguard Up-Rise II 48 Photo Backpack also works, per this video.