What do you consider the quintessential PlayStation games?
 

I now have a PS3, primarily for use as a Blu-ray player, but I got one of the old backwards compatible models specifically because I've never owned a PlayStation before and I know there's plenty out there I've been missing out on.

So I put it to you guys, what do you consider Required Playing for PS1 and PS2? Please keep it to PlayStation-exclusive games only, if you don't mind. And preferably, y'know, attainable ones.

(While I'm at it, does anyone know why my controller won't sync up with the console? USB cord or not, pressing the PS button just makes the lights flash for a bit--then nothing. Internet troubleshooting has only resulted in giving me a headache... Do the lights still flash if the battery is dead?)

But yeah. Games.

Uhm.

This is a bit more than you're asking and I'm sure that some/lots don't meet the requirements but here ya go.

It's a good start. :3 Though I'm looking for PS2 games as well, which aren't on that list.
I should probably mention, though, that RPGs aren't really my thing. I've never even managed to finish one...

Get Megaman Legends 1 and 2 and the Misadventures of Tronn Bonne. You will love me.

Also, Tales of Destiny is fun, not to mention Xenogears has an awesome plot and if you can grin and bear the first part of the second disc then it is a doozy of a game and the obvious Final Fantasy stuff.

If you like Zelda you must pick up Alundra. Resident Evil 1-3 obviously, the 5th installment is coming out... you should see where the series came from.

Hmm... platformers... OH! Tomba! Probably one of the wackiest, silliest, and just down right fun games ever. It is an exploration game at heart and I spent about 100 hours looking for everything! This game was made by the guy who created Mega-Man!

Front Mission 3 or Final Fantasy Tactics for the SRPG fan out there. They are probably the most popular from the PSX era, but there are others. Front Mission 3 has a branching storyline, and Tactics just has awesome gameplay and memorable characters! Other good SRPGs include Vandal Hearts, Ogre Battle, and Vanguard Bandits.

I always recommend Parasite Eve 1 and 2 to someone who wants to play PSX games. They mix the Survival Horror genre in with RPG elements and are just really good games, despite the short length and a few minor problems.

I'll add more as I think of them, the PSX is tied for my favorite system with the SNES, so I have played LOTS of games!

Kingdom Hearts 1 and 2 are awesome.

The newer games that are out for PS2, I don't know so I won't reccomend.

Okami. That's really all I've got to say.

Freedom Fighters for PS2

P. Eve can never get enough PR. Neither one of them.

Psychonauts. MUST HAVE.

I'll probably have more later.

Shadow of the Colossus

Ico

Crash Bandicoot 3: Warped

The three Metal Gear Solids

God Hand

And I don't know. The PlayStations were always my JRPG machines, and you don't seem to like that genre.

Final Fantasy IX.
I enjoyed the original Syphon Filter (sp?), as well as any fighters that came out for it.... always enjoyed a little Virtua Fighter

PS2
Quintessential (regardless of genre): These are the games I'd be all "Bwuh?" to hear you've never played.
Xenogears
Final Fantasy Tactics
Mercenaries: Playground of Destruction (was this cross platform? I don't remember)
Kingdom Hearts (at least the first one)
FFXII (others as well, but this is the least jrpg-ish, and thus the only one I would really suggest to you)
God of War
Devil May Cry
Devil May Cry III
Shadow of Colossus (even though I don't like it that much, I can still appreciate it)
Katamari Damacy
GTA: San Andreas

RPGs you may still like All of these have semi-action game-esque combat.
Radiata Stories
Star Ocean: Until the End of Time
Shining Sword EXA (Not a great game, but fun mindless entertainment. Plays like one of the top view zeldas but with level ups and equipment)
Full Metal Alchemist (there's two of them, both are pretty great and not turn based at all)

Action Games
Contra: Shattered Soldier.
Lego Star Wars (both of them)


And... yeah I'm tired of listing games now.

Screw it.