My tastes are a bit odd, so I'll keep my list the ones that seem to feel the universal love.
Resident Evil 4 - Great game all around, best controls I've ever played. The G4TV people named it the best game they have ever reviewed. You could also look into Resident Evil: Code Veronica X which is also a great game.
God of War- Sick fighting and sick graphics
Grand Theft Auto: 3/Vice City/San Andreas: Controversial, vast, and very enjoyable. So much stuff to do in every game.
Metal Gear Solid: 1/2/3 - Not only are these some of the best action games around, but the story held within every game is complex, mind-blowing, and at times even beautiful and touching (especially 3). Each game can be played alond and you would still understand what is going on.
Those are the ones that are just overall great video games. The following are not for everybody.
Final Fantasy (7-10, 12) - Great overall game series but ones that have to grow on you, since they are roleplaying games. The ones with the best stories are the lower number ones, thus only have PSX graphics which are a turn off for new coming gamers. On the contrast, the new games have relatively less -epic feeling storylines in the creater's desire to develop more adult storylines. These are nevertheless great games, but I would suggest renting one of these (probably X before XI as it gets into things faster).
Kingdom Hearts - Its a game series that is the offspring of the creaters of Final Fantasy and Disney which, while seeming like a horrible idea, produced a rather enjoyable set of games (to the point of making a sequal and even another one coming up). However, I would say one would have to be into FF games to really enjoy this so try that before giving this one a try.
Katamari Damacy - Very fun but very Japanese, test first.
Prince of Persia games - I do not know much about these, but they seem very fun from my first experiences (though i was enthralled in WoW at the time).
