Ok.. I've been living in the 3 year old game territory for some time. I've played cheesy to excellent games in that age bracket, most of which can be had for around or under 10 bucks
Indie Games (These are those cheapo but damn fun games)
Altitude - 2d, multiplayer or bots plane flying, shooting game. Includes Capture the flag and a "soccer" like game modes, very fun to burn the time or to play at a lan with friends.
Beat Hazzard - Had 2 player mode, never used it. Similar idea to audio surf, much more fun. Your music changes the enemies that spawn, and your weapon. So faster music makes it easier in a way, and slower gets harder. Very cool game, addictive.
Braid - This game will hurt your brain at times, total strategy/puzzle, VERY unique and different. There is a demo on steam, try it first. But if you like games that screw with your mind, this is it.
Others:
Borederlands - Yea its got guns, but its fun none the less.
Fallout - This easily falls into the 3 year old game, but serious its one of the best games i've played. Bethesda studios makes it, same guys who made Skyrim. Its first/third person shooter/melee, but don't let that fool you, its an RPG. The V.A.T.S in game "targeting system" basically lets you turn it into a turn based "roll of the dice" kind of game. So if you dont feel like shooting at someone, you don't have to. If you do feel like it, you can. This would be my first suggestion to you in case you haven't gotten it. I've only played in on PS3 unfortunately, but of course you can get 1000's of mods for the PC version and better graphics
Assassin's Creed - Was mentioned by someone above, good game. I got it for the PC after playing it on my brothers XboX a few times, can be had for under 5.00 on Steam sales. I think I picked up on it for something like 3 bucks. Recommend hooking up a XboX controller to your PC if you get it, makes the game that much more enjoyable.