Ah, Timesplitters. Any past the first one is fuuuun times, and that's for sure. "The moooose is loooose!"
I found the GTA games pretty terrible on the PS2, but maybe that's just me.
The .hack// series is amazing. I hate JRPGs because they're too overdramatic, overcomplicated and cartoony, not to mention usually punishingly hard. The .hack series is a beautiful exception. The first series is amazing until the stunning finale to episode 2. After that the gameplay becomes repetitive and the amazing story slows to a glacial crawl.
.hack//G.U., the new series, fixes all those problems as well as making combat worlds better, more interesting characters, great animation and monster design, a sweet upgradable steam bike, and did I mention better combat? I don't think I've ever had so much fun racking up combos, using skills and chainsawing my enemies into submission. Might not be easy to grab the first part, though. There are 3 episodes.
Good on you to have Parasite Eve. I love that game an unhealthy amount as well.
The Dino Crisis games are incredibly fun (if silly enough to make a paleontologist hang herself), with combo counters, multiple guns and big fights with bigger dinosaurs. You'll never look at a T-Rex the same way again.