A lot of people here seem to see JRPG's as crappy Final Fantasy-ripoffs, and even though that may be the case with 80% of them (Sturgeon's Law) there are some fantastic titles among them. Some of my favourites:
-Paper Mario series (an affectionate parody of the Mario franchise that has fun action-based battle system, clever dialogue, and some very memorable moments)
-Earthbound (a twisted postmodern Japanese look on American society, very funny and weird, definately an experience you won't forget)
-Mother 3 (hard to explain, but this pretty much convinced me games can be art)
-Tales of Symphonia (this might initially look like a very standard RPG but slowly many of the cliches get deconstructed. It also has a great battle system and likeable characters. It keeps you hooked for many, many hours)
-Chrono Trigger (I doubt there are many people who haven't played or at least heard of this classic)
Oh yeah, and which gamer my age didn't grow up with Pokémon?