I've found that clear packing tape works great in many instances. For those stupid stickers that just keep pulling apart that Gamestop slaps on every case, I take the insert out first to avoid denting it. I then peel/scratch off whatever part of the sticker I can. Once that is done, I put a piece of clear packing tape over the label and gently rub it until it sticks to remaining label bits. I then hold the case so I am "pinning down" the clear outer sleeve to the case itself and give the tape a good yank. 9 times out of 10, it pulls a significant part of the sticker off. I may have to give it a few tries, but this method works great. It also pulls any gooey bits off that may have been left behind while you were trying to peel the sticker off to start with.
I've also used this method on the top part of game discs and cartridges (not on the labels though). I've found that alcohol or any other agent besides water can actually cause the ink on the disc surface to smear. The copy of Alundra that I picked up at the pawn shop had one of those rental stickers covering the entire top of the disc. When I removed it, it left quite a bit of sticky goo behind. Dabbing packing tape on & off for about five minutes, I was able to get all the gooey stuff off.
For realllllly old stickers that just seem to disintegrate into powder when you try getting them off, I use a damp paper towel and rub it back and forth over the sticker. Once it has absorbed a bit of moisture, I then use the packing tape trick. Usually works.