1. Everything by Atlus. This means Persona 3, Persona 4, Shin Megami Tensei: Nocturne and both Digital Devil Saga games. Haven't played the Raidou games, but those are more real-time and weird.
I think you'll particularly enjoy the combat of Nocturne and Persona 4, since Shin Megami Tensei uses some of the same ideas as Pokemon (despite preceding the franchise by quite a few years). You gather monsters/personas and fight with tactical turn-based combat. There's also always an intriguing plot, great design and amazing music.
Persona 3 is also good, but the version on the PS2 doesn't offer full control of your party members, which is a bit of an impediment.
You should also consider that Nocturne is considered to be balls hard by modern standards, so if you're unfamiliar with tough JRPGs then Persona 4 might be a better entry point to the series. Unless you dislike wordy games, that is. Compared to Persona 4, Nocturne is a silent film. They're both very well-written, but P4 by its nature has more opportunities for dialogue and characterization.
2. Anything by NIS. This means Disgaea, Soul Nomad, etc. These are more SRPG than traditional JRPG, but they're fully turn-based and have plenty of tactics and humor. A lot of fun.
3. (Xbox 360) Tales of Vesperia. Feels like a completely unashamed tribute to oldschool JRPGs in the FFIX vein. Despite that, it has some interesting real-time combat. Great characters too. On the surface, everything you hear about them sounds simplistic and cliched, but they're so much better than what you're picturing. Trust me.
4. (Xbox 360) Resonance of Fate. Tactical RPG. In a way, this is like Valkyria Chronicles shrunk down with more combat options and customizations available to each of your three units. The story is completely impenetrable and convoluted, but the characters are so fun that you probably won't care. Combat takes some getting used to, at which point it goes from "okay" to "fantastic".