These are my five, but there's no specific order to these.
PSIV - I think everyone has covered the reasons on this one already.
Dragon Quest VIII - A perfect blend of classic and modern gaming. I played a game made after 2000 and felt like I was reliving a NES game. For an old school gamer, this is joy.
Chrono Trigger - Excellent execution of an excellent concept. I love the way they added different endings at each point in the game.
Super Metroid
Spider-Man on PlayStation - When it came out, it was called the best superhero game ever. It is. The designers captured the spirit of comics, had fun with it, and it made the game a great experience.