Two games I can recommend with zero qualms: Disgaea: Afternoon of Darness and Fire Emblem: The Sacred Stones.
Disgaea: Afternoon of Darkness is a turn based strategy RPG with some great humor and a protagonist that you will love to hate (or at least, love to be mildly revulsed by). It has some of the best American voice acting I've ever heard (save for the fact that you have to push "X" to get to the next line. It breaks the flow.) and some of the special moves, especially the character specials, are really flashy and pretty.
Fire Emblem: The Sacred Stones is another turn based strategy RPG, but it's on the Gameboy Advanced (or at least the one I played was on the GBA). It isn't as visually impressive as Disgaea (which is on the PS2), but that's only to be expected given the difference in platforms. I find it very difficult to explain to people who have not played Fire Emblem what is so compelling about it, just know that this is a hearty recommendation coming from a huge strategy fan.
EDIT: Wups, make it three! Kingdom Hearts 2 is a great real-time JRPG if you can get yourself past the three hour long intro. I haven't played the first one in the series, but I have played Chain of Memories and 2, both of which impressed me greatly.