try warcraft 3 it a great game and some of the high demand games are, dead or alive 4, gta:san andreas, need for speed most wanted, wow, battlefield 2, f.e.a.r., prince of persia: the two thrones and many more.
A goog choice is Star Wars: X-Wing Alliance Knights Of The Old Republic 1+2 Jedi Knight 3: Acadamy and so on... ^^ gez zack1987
When I first started, I thought it was great too since what attracted me was the skills system, but it turned out to be a total flop at higher levels. They also had major lag and hacker issues which made me quit. The game did look lovely though. I liked the graphics even on my ancient PC. I would also recommend Warcraft 3. The custom maps people churn out keep the game going as well as the automated ladder system. @DanK: Are you looking for online multiplayer games or single player ones? A genre would help too.
Warcraft III Frozen Throne! You can also play DOTA if you are bored with the normal games (which was like starcraft). Heroes of Might and Magic V is also quite interesting if you like strategy games.