I usually use the sticker I peel off, especially if it has some decent adhesive. Problem is that certain stickers work really well, which are more likely to leave residue when you remove them to begin with, while others are fairly poor, although they tend to leave no markings whatsoever. Just keep applying sticker and removing with a quick snap or so until the sticker starts filling up with extra junk and becomes useless. Be careful, because with some particularly powerful stickers there's a tendency to leave more behind than what you pick up. It's rare, but you'll know those sorts of stickers when you see them.
Security stickers function the same way. They are much more of a rarity but can be found on a lot of independent store merchandise, especially if you're buying old games from ancient video stores. These tend to be the kind that leave some sort of marking like "VOID" or whatnot when removed too quickly. You can take them off if you have patience and go very slowly for about five minutes, but if you have some residue from one of those I suggest taking large parts off with your fingernail (especially if it's medium in length or just plain long) and then using Goo Gone in order to remove the rest.
Another interesting tip, even though it has nothing to do with stickers, is that you can remove Sharpie markings from games with a moderate amount of effort with...Goo Gone, of all things. I once removed Sharpie from half of an NES cart that I picked up used. Granted, it did take around 20 applications of Goo Gone and a good 20 minutes of scrubbing here, there, and everywhere, but afterwards it looked like nothing ever happened in the first place.
