I actually had a post done up two days ago while my computer was acting up with me. Suffice it to say it was lost and it took me until now to be bothered retyping it all (it's long ok).

Blood Omen: Legacy of Kain - I'm talking about the PSX original here. Despite the rediculous amount of slowdown in this game, it was a very fun 2D adventure game. It had one of the coolest, most in-depth worlds of any game going, even today, along with the best anti-hero in gaming. Not too mention sucking someones blood from ten feet away for the first time was awesome beyond words.

Star Wars: Starfighter - I think this one got kind of overlooked coming out not long after the PS2's launch. It was a really cool flight combat game, and I liked it more than the Rogue Squadron series myself. That's some pretty high praise right there.

Ring of Red - Another title that got lost in the early days of the PS2, and suffered the misfortune of coming out around when Onimusha came out. It's a very cool strategy game involving a variety of mechs, and is probably one of my favourite strategy games of all time. I put more hours into this than I can count, even neglecting food and drink for hours on end because I was so caught up in the game. Well worth checking out if you can find a copy.

Edit: Just noticed ThundagAuron mentioned Jazz Jackrabbit 2, and I've got to agree with that choice. Awesome game.