JRPG, I'd recommend... (bias, weeding out a lot of things based on my semi high standards in one manner or another.)
-Disgaea 4, been awhile since NIS got me to feel for their characters. Very funny story with an interesting cast that can stand up to the first (Which is my favorite jrpg/strategy game).
-Tales of Xillia, has a really good battle system, I've gotten a little bored of the story and stopped (I have to go back) but the story is pretty good (been awhile since I had this much fun in a tales game (Phantasia story randomly dropped so many times I kept getting bored and I hated Legendia overall (the last 2 I played)).
-Tales of Graces F, exist, but I know nothing of this game... but it's stays at 40-45 dollars (released before Xillia, and on gamestops website is selling for 8 dollars more than Xillia).
-Tales of Symphonia, my favorite Tales game (and in my top ranks for overall favorite game) has been ported to ps3.
-Final Fantasy 10, has been ported too. If you missed your chance to play/own it and don't mind buying 10-2 along with it. It's unfortunately worth the purchase though >_> (for me) I never owned a copy of 10...
-Persona 4 Arena, (if you played persona 3 or 4 it's continuation of more story might interest you).
-Catherine, not quite a rpg it's more of a puzzle/visual novel, but it's quite fun.
-Demon Souls, I'd say with the improvements made in Dark Souls it's kind of pointless to bother with Demon Souls (Yes I am still pissed about the twin gargoyles and 5-1, those were so frustrating), but there are rumors of a Demon Souls 2, so it may be necessary depending on how much story they will pull from predecessors.
-Valkyrie Profile, is worth checking out, it was a new and interesting battle system for me that was quite fun (there were a lot of things I would have preferred changed or improved on, so I always wondered about the sequels). Story was so-so to me.
-Star Ocean: Last Hope, just felt like they were trying to recreate Till the End of Time (Which I idolize for it's design) with a more complicated battle system, I didn't like it, but I also didn't get very far, so it's fair to say that I really didn't get to the fun parts. To me though it's just another of Square's.. "meh".
-Nino Kuni, I hear a lot of good things of it. missed that in op's post.
-White Knight Chronicles, is supposed to be worth it, haven't played yet but was told to buy the HD collection of 1 and 2, that 1 was badly designed (in a way I forgot) and that they redesign it in the hd version.
-Mugen Souls, if you can find it, it looks interesting. I don't expect much from the story, but the heavy grinding and character creation/customizations interest me(if your into that and chibi(ish) characters) never played it though so I don't know of it's quality.
-Persona 2 Eternal Punishment, I still have to beat 2 but I didn't know this was for ps3... I have to play it sometime.
-Final Fantasy 6, too... I'll have to stick to emulator for now.
-Eternal Sonata, though I never played it, it seemed to do decently. Never heard it praised but never heard it bashed.
-Odin Sphere, was ported too... I can finally play it! (I don't know if it's any good, it was just one of the jrpg's from the ps2 era that I was never able to buy.)
-La Pucelle: Tatics, was also ported for ps3 (2nd favorite jrpg/strategy game).
-Xenogears, I have to play this one too... emulator for the time being though...
-Parasite eve 1 & 2...
-Chrono Trigger...
-Breath of Fire 4...
-Legend of Mana...
-Grandia, (always wanted to try the first).
Note to self: so many ports I have to play...
-GrimGrimore, while the story was nothing really strong, it was a really fun rts/rpg, when you summon a dragon you felt like a boss and when you summoned 4.... you start laughing maniacally. It's cool they ported this, though I already have my copy.
I'll leave action games for other people since my list is too long and I'm still in the process of acquiring more of them for ps3.