Actually obscure but awesome games
Gitaroo Man
Sky Gunner
Silhouette Mirage - It's Gunstar Heroes meets Ikuruga
Robotech Battle Cry - Certainly flawed game but it's got some really good segments and is pretty challenging, Vs. mode is really fun if you want to play with a friend.
Um Jammer Lammy
Fragile Dreams
Evil Zone - Also a cheesy awful game, but it definetly falls into that "so bad, it's good" mentality.
El Shaddai: Legend of the Metatron - So this is what an acid trip is like...
Incredible Crisis
Mech Commander
Colonization - It's pretty much Civ2 but why the hell not?
Jade Cocoon - Even I forget this fun Pokemon rip-off
Amplitude

Not obscure, but damn I'm surprised how many of you have never played any of these
Xenogears - It's on PSN for crying out loud!
Suikoden - Any of the numbered entries, though Suikoden II, III, and V are probably the best entries to play
Breath of Fire - Any of the five awesome titles are good, though II - IV are the most popular.
Persona 3 and 4 - I mean come on... There have been three versions of P3 released and P4 is getting a port on the Vita, giving you two ways to play this. You have no excuse, they're even on the PS2 for crying out loud, so you can't say you can't afford the system!
Vagrant Story - Also on PSN now. Probably Matsuno's finest game.
Shin Megami Tensei III: Nocturne/Lucifer's Call - I've noticed this game has become a bit easier to get a hold of nowadays. At least where I live.
Digital Devil Saga - are you getting the hint EoFF, I want you to play some MegaTen dammit!
Legend of Mana - easily one of the most underrated entries in the series. You can even do co-op and adjust the games difficulty.
Front Mission 3 - Its a turn based SRPG, with giant robots!
Catherine - Oh hell yes

I'll probably remember more at some later time...