There are a few games I really suggest to you. The PS2 actually had a very good linup, so I'm sure one of these games will strike your fancy.
Shadow of the Collossus: This game is really something else. I don't even really know what genre I'd put it in... Adventure, RPG, and with some elements of Puzzle. SotC is basically a huge boss-gauntlet that lasts through the whole game. You have to fight 16 giant collosi, and when I say giant, I mean giant. They're so big that you have to find ways to climb up their backs to get to their weak points on their heads. It truly is an adventure of epic proportions. If that sparks your intrest, I highly suggest you check that one out.
Kingdom Hearts Series: Kingdom Hearts is arguably the best RPG of all time. In fact, I think it's close to perfect. It's developed by Square, (now Square Enix) which also developed the Final Fantasy series, and the Chrono Trigger series, although KH is not turn based. Hell, it not being turn-based is one of the reasons I like it so much. No waiting, just plain-out brawling. Square also got the rights to certain Disney movies and characters, so there are worlds such as Wonderland from Alice in Wonderland, and Mount Olympus from Hercules. So once again, if you're into that type of thing, I really suggest you check that one out.
Seeing as you already own those two games, here's one that I think is a must-have for all PS2 owners.
Star Wars Battlefront: I think that the original blew the second Battlefront out of the water, so we'll be talking about the original. This game takes place in the Star Wars universe, so you'll get to play as Clone Troopers, Rebels, and even Stormtroopers. It's a third person shooter with a lot of strategy involved. There's many game modes, such as Capture the Flag, a mode where you try to capture all the points, and a mode where it's just plain-out fighting.
That's what I think.
