I play mostly rpg's and fighting games, so I can toss out some of my favorite rpg's, since they *usually* have a pretty good story.
Shadowhearts
Shadowhearts Covenant (best of the trilogy)
The 3rd Shadowhearts game, From the New World, is ok. Its certainly the most polished gameplay wise, but the story isn't as good, so I don't recommend it as much (and doesn't feature the same main character as the first 2, so it is skippable if neccesary)
(or was that supposed to be Shadow Hearts instead of Shadowhearts? You'd think I'd actually know, since Covenant is one of my favorite games ever)
Xenosaga 1-3
Ar Tonelico 1 (the second game is ok, but it has a game crashing bug, which may or may not affect you, so it's harder to recommend it)
For other Gust games (imported by Nis), you have the Atelier Iris (1-3) and Mana Khemia (1-2) that are good as well. Of those 5, Atelier Iris 3 is the weakest link, although not a terrible game.
I own Suikoden 3-5, but have only played 4 and 5. 4 was ok, if nothing remarkable. 5 was pretty good though. (I'm assuming I'm correct on the numbering system here. Don't have the games in front of me, so I won't swear to it)
Shin Megumi Tensei - Persona 3 and Persona 4 are must own, imo. The other Shin Megumi Tensei games, like Nocturne, Digital Devil Saga 1 and 2, Devil Summoner 1 and 2, all have good stories. But, the game play is a mixed bag. I still would recommend them, but Persona 3 and 4 certainly were the most complete packages, including story and gameplay.