Oh man, this thread was made just for me. In no order...
CANNON SPIKE:


Way fun with 2 players, a classic-feeling beat'em up. Just so fun.
BOMBERMAN ONLINE:

Used to love going online and blasting fools/getting blasted by fools

SHENMUE and SHENMUE II:

Rocked me awesomely, the whole way through. Picked up the second via UK import and played with a boot disc, and it was like, even better. For those of you that liked the original, but still haven't experienced Shenmue II, I recommend it highly; though, it'll be bittersweet, since it seems Shenmue III will never happen.

SKIES OF MOTHERFUGGING ARCADIA:

Amazingly fun to explore, unique battle system, fine story and characters.
JET GRIND RADIO:

Idunno, it was just plain fun and a fresh idea for a game. Psh.
SPACE CHANNEL 5:

Wacky!
TIME STALKERS:

Underrated, probably because about 15 people nationwide actually played it. Was a solid RPG, interesting story/plot concept.
POWER STONE 2:

Still my favorite fighter ever. Fiercely fun with 4 players.
PHANTASY STAR ONLINE:

My goodness was I in love with this for a long time. Never paid for the online, either. Like, I joined after its prime and I guess their billing system was wonky or something, because for those 6 months or whatever, I played but never got a bill or anything. Was kinda funny. I would have gladly, but...never got charged.
NAPPLE TALE:

Very good action RPG in the vein of Gurumin (recently released for PSP).
SOUL CALIBUR:

The SOUL STILL BURNS!
Man...What a machine...what a bunch of classics...
Oh yeah, and Grandia II. Almost forgot. Much love.