Shogo: Mobile Armor Division, which was a FPS actually developed by the same people as No One Lives Forever. Cool game that most people I've mentioned it to never heard of it. It had you playing on foot half the time and the other have the time in a giant robot. Both modes played like a FPS though, it was pretty sweet. I think it was the first Lithtech Engine game.
For RPGs, Lunar: Silver Star Story Complete. A simple but well delivered story. It's probably my favorite RPG.
Another RPG worth mentioning was Kights of Xentar. It had two versions, a T rating equivalent(rating system didn't exist yet I think) that was censored and sold in stores like EB (where I got it) and a AO version sold through mail order. Never played the uncensored version, but the version I had was hilarious. It was really funny all the way through.
Not sure if it was unsung but Thousand Arms was also a good RPG not many people seem to know. PSOne Atlus RPG that had you power up your weapons with minigames and a dating sim system. The writing was really funny on this one too. The graphics where good for the time with 2D SD sprites on a 3D overworld and large detailed character sprites on the battle screen. And plenty of voice acting.
And finally a couple fighting games.
Melty Blood, a 2D 1 on 1 fighter for Windows, was never officially released in the US, but there was a fan translation patch. I think it got arcade and PS2 releases in Japan.
Lastly, Evil Zone, a flashy 1 on 1 anime themed 3D fighter for the PSOne. The few people that have played this game either love or hate it. It had a simple control scheme involving only the D-Pad and two buttons, preforming different moves depended on what direction you were holding on the D-pad and distance from the other player. It was very different from other fighters at the time. The things I liked the most about it though was that the Story mode actually had a story for each character that played out in different styles. One guy had "Next time on!" like intermissions between each fight and another had lead in and lead out conversations with the other fighter or a 3rd party. Also, it's special moves were all cinematic, like a summon from a Final Fantasy, the first time you did them each round. Might have to break that game out again sometime soon...