Oh man...only three?? I don't know if I can do that. This is in no particular order.
1. Arc the Lad: Twilight of the Spirits. The only Game in the series that I enjoyed, and I REALLY enjoyed it.
2. Star Ocean 3. The only major drawback for me with this game would be the voice acting, but you can turn that off if you so desire. The intertwining of Sci-fi and fantasy is quite interesting and the sheer amount of background (which is accessible in-game) that this game has is close to overwhelming levels.
3. Legaia 2: Duel sagas. I had so much fun trying to figure out the correct combinations for the power moves in this game. I haven't seen a system similar to this in any other RPG.
I think if I had to pick one based on story alone though, I would have to go with Grandia 2. There is a really dark and gritty story in that game that just grabbed me and wouldn't let go. A lot of the bosses have a creepy aesthetic to them as well.
But there are so many other great RPG's on PS2! Definitely the best console to have if you are into RPG's by far. Not to mention all of the great ps1 RPG's that can play on it as well.
---------- Post added 2013-01-11 at 10:13 AM ----------
I tried and tried to get into the xenosaga games, but my GOD the cutscenes in those games are just unbearable! Not the quality or anytthing mind you, but the sheer amount of them. There are probably more cutscenes in that series than any other RPG to date.