The vast majority of games are just a disc, therefore there's nothing to stop you selling/buying second hand.
Pretty much all single-player games will not have an issue of it's second hand or now.
However:
Multiplayer games are getting a bit more difficult. For example Battlefield Bad Company 2 has a 'VIP' pass that comes with new copies of the game that gives you a load more maps to play with, whereas if you bought second hand, you wouldn't get those maps. You can usually buy the extra content via Xbox Live to top your game up to what you would get retail (so you can buy the BFBC2 VIP pass for 800MSP). Another example is Mass Effect 2, there's a bunch of DLC that you can only get with new copies of the game, but you can buy it if it's second hand.