Devil May Cry : A great action/adventure single-player game that puts a heavy emphasis on the action. Decent replay value as well, with lots of things to unlock.
Dynasty Warriors 3 : Another game that provides well in the action category. Choose a warrior and take him (or her) through one of many epic war battles, fighting your way through thousands of soldiers and enemy generals. A second player can join you on the battlefield as well, or you can both go against each other in the Versus mode. A TON of replay value here, with many characters, weapons, and items to unlock.
ICO : A beautiful adventure, and nothing short of a masterpiece. There\'s very little slice-n-dice gameplay here, but there are a plethora of puzzles to wreck havoc on your mind. Not much to unlock after you finish the game, but it\'ll be hard to just throw it aside with little intention of experiencing the story again. You should at least rent this one to give it a try.
Those three are my highest recommendations. Some other great games include Red Faction, Silent Hill 2, Onimusha, and Ring of Red. Check them out if you\'re not interested in anything else.