Wait one minute...Deus Ex was on the PS2? How did I not hear about this? I have GOT to find that game, especially since Ion Storm no longer exists.
That's a nice PS2 package (what FF is it?). Both Ico and Shadow of the Colossus are good platformer/puzzle/action/adventure games (that was the only way I could describe them), though Ico is a bit rare. And I'd put Kingdom Hearts at the front of your list...it's amazing. Xenosaga is infamous for it's ridiculously long (up to 30 minutes), unskippable cutscenes. If you want to take that plunge, be my guest, but be forewarned. You could also try the Shin Megami Tensei games. Disgaea is another quirky RPG, and it's PSOne predecessor, Rhapsody: A Musical Adventure, is ridiculously hard to find, but a unique and fun game (though a bit of an acquired taste. Valkyrie Profile and Vagrant Story also fit in that same category (both PSOne). Also, (if you can find it), Xenogears is a classic (though rare and still $30+). Shadow Hearts is another cool RPG with a unique battle system. The entire Grandia series is worth playing, as well. Suikoden is another quality series (though they all seem a little the same; just play Suikoden III. The Star Ocean series is also worth a play. Finally, Rogue Galaxy may be the last great PS2 RPG. Let me warn you, I have played most if not all of these, but in small doses. Most of what I know comes from reviews and peers. Also, most of these games are quite rare.