In chronological order, since I couldn't possibly rank my top 5:
1) X-Com: UFO Defense
It's staggering how complex and how perfect this game is, both in the strategic component in the tactical one. Even more staggering is that it's never been duplicated, not even by the well-publicized remake, which is excellent but nonetheless inferior.
2) Chrono Cross
Best soundtrack ever in a game, story was dizzyingly complex but also heartfelt, and the game was rife with small innovations like poste-battle healing and fast-forward in new game+. I think I've played it through about 6 or 7 times.
3) Valkyria Chronicles
Everything about this game is beautiful. The art, the way the story is presented, the gameplay. I didn't blink at playing it through again immediately after finishing it the first time, and getting the top rank on all missions was an obsession.
4) Demon's Souls
Gaming perfection. A lot of people seem to prefer Dark Souls, and I like that game as well... but I thought the environments and bosses in the first entry were more frightening and more intimidating, which made them more fun to conquer.
5) Monster Hunter 3 Ultimate
The combat gameplay is just so excellent, and getting yourself the perfect weapon(s) and then hunting yourself the perfect armor set to go with those weapons is endlessly satisfying. Probably the greatest co-op game ever made.
Stuff that was very hard to leave off:
Powerball
King's Field 2
Final Fantasy 7
Final Fantasy 10
Romance of the Three Kingdoms 8
Super Mario Strikers
Def Jam: Fight for NY
Okami
Burnout Paradise
Uncharted
Xenoblade
FIFA (whatever the latest is)