Endless Paradigm

Overall, I didn't play that many games.  Ones I did play for more than about 5 minutes (from memory):

Medievil (only played first 2-3 levels, seems like a decent game)
Wipeout Pure (never was good at it)
Star Ocean (completed it, though I think I like the SNES version better)
Corpse Party (completed it, though the game mechanics were painful at times)
Loco Roco (played first few worlds, good game, but never completed)
Project Diva series (probably played this the most)
K-On Rhythm game (similar to Project Diva)
Final Fantasy IX on PSX (text was a bit too small and hard to read, so stopped after a while)
DJ Max Portable (didn't play it much, have gotten into the PC game more)

All the Ys games
Crisis Core
Persona 2 EP
Grand Theft Auto Liberty and Vice City Stories
Kingdom Hearts BBS
Kenka Banko Badass Rumble
Ultimate Ghosts n' Goblins
Castlevanis Dracula X
Tekken
Wipeout

Still more but I think these are the absolute

7th Dragon 2020
Tactics Ogre: Let Us Cling Together
Dissida 012: Duodecim Final Fantasy
Castlevania: The Dracula X Chronicles
Star Ocean: The Second Story
Valkyrie Profile: Lenneth

I'm sure I missed a lot, but those are the ones that I remember the most.

Tales of Eternia
Persona 3
Dissidia (both. forgot the other one)
tekken 6
gods eater
dj max
naruto ultimate ninja heroes and 2
n+
cladun this is an rpg
fight night
flatout
gta chinatown wars
gta vcs
gta lcs
k-on
kingdom hearts bbs
phantasy start portable and 2
shadow of destiny
god of war
and many mooooooore.

Tekken
Phantasy star portable 3
Patapon 3
Gods eater burst
Monster hunter portable 3
God of war: Chains of olympus
Half minute hero
What did I do to deserve this my lord!?

Let me think:

Both 3D GTA games were great (Liberty City Stories and Vice City Stories)
If you're into casual sports games, then I can highly recommend Everybody's Golf 1 and 2 (Hot Shots Golf in the US) and Everybody's Tennis (Hot Shots Tennis)
Corpse Party was a pretty interesting experience. Book of Shadows was a bit chocolatetier.
I had good fun with Burnout Legends.
As far as JRPGs go, Ys Seven wasn't bad. Of course there's also Persona 3 Portable.

But it's been a while.