The top RPGs I would suggest are:
1. Dragon Quest VIII
2. Dragon Quest V (Import)
3. Suikoden III
4. Odin Sphere
5. Final Fantasy X
6. Final Fantasy XII

Pretty much in that order. There's other RPGs such as Persona 3 + 4, Grim Grimore, Dark Cloud 1 + 2, Multiple Tales games, La Pucelle/Disgaea/Phantom Brave, Suikoden IV and V, Final Fantasy X-2/Final Fantasy XI, Valkyrie Profile 2, etc. But I either didn't play them or didn't like them (such as is the case of Suikoden IV and V or the Nippon Ichi SRPGs). So you should look them up yourself. The ones above I would definitely suggest you get however.

Rogue Galaxy! Definatley

persona 4
final fantasy X and XII
Valkyrie profile

Well, since this thread is already boiling down to a list of people's favorite PS2 RPGs (though that was to be expected), I figured I'd mention a place that, while annoying, can sometimes be a cheap place to find PS2 games used: gamestop.com . Yes, the evil empire. I've seen games that go for $15-20 at other places for $4 in their used bin, and a couple of those rare games can be in the realm of $30 or so at GS, assuming they have them in stock.

But recommendations... hah, sure, I'll chime in, too. I'd agree on the Persona games (3FES and 4), and would also recommend, if you like those and want something harder (or without the social link aspect), Digital Devil Saga 1 and 2. The Tales series is also good if you're looking for more action (which you mention in the op), and I can easily recommend Tales over Star Ocean 3. FF12 might work, since it's more action-oriented than 10 (I heavily recommend against 10, BTW.), but it still might be hit-or-miss.

Dark Cloud 1 and 2.
Final Fantasy X
Dragon Quest VIII
Kingdom Hearts 1 and 2

Those are some of the best.

Tales of the Abyss, its expensive though.

AND! Ar tonelico, Ar tonelico II.
Aside from the graphics, the games are amazing. (well, at least the second one, I haven't played the first one but I hear its as great as 2)

Tales of the Abyss
Star Ocean 3
Rouge Galaxy
Kingdom Hearts series
Valkyrie Profile
Dark Cloud series
Hack G.U. series

Those are some of the action rpgs I can recommend.

For other great rpgs:

Digital Devil Saga series
Xenosaga series
Persona 3: FES
Final Fantasy X
Disgaea: Hour of Darkness

I second Dark Cloud 2, Kingdom Hearts and Kingdom Hearts 2.

i was there for 5yr's until my ps3 brokedown on me. it fail 10x and the sad part is i never dropped it so i missed ourt on all but one. FF 10! i spent 180hr's (when i didn't have a job) playing this game and im still not done. yes i beat it.

u cannot forget Suikoden 3 , 4 and 5.
really good rpgs for the PS2.