Persona 3 and 4: I preferred 4 since the super "dark" theme of Persona 3 didn't really mesh very well with various gameplay and story elements. Still an amazing game but I just prefer Persona 4 so I would try that and if you like it and want more then get Persona 3. All the aspects of Persona 4 from music to graphics to setting work together VERY well in order to make an experience that's more then the sum of it's parts. Mega points for making turn based combat FUN!
Xenosaga 1 and 3: Gameplay is boring, if not broken or frustrating, story presentation is AWFUL(cutscenes so long they had to save points in the middle of them like some sort of intermission...) and the subplots are often times uninspired but the main story itself is so good I was able to overlook all these flaws and value it more highly then any other game I've played. Just don't go in expecting any fun. Seriously, not a drop, there's none to be had here. The fun is dead. DEAD!
Star Ocean: Gameplay is very fun and there's TONS to do, story is usually pretty bad but it doesn't take itself too seriously so it's not all that bothersome.
Disgaea: Love it or hate it on this one. SRPG with heavy anime influences that enjoy's parodying/deconstructing/satiring pretty much everything at one point or another, Japanese culture, video games in general, and "hero stories" being the most common targets. Silly and unique from start to finish and generally really funny to boot.
There's lots more but these are my "standard" recommendations.