I can't believe nobody mentioned Tony Hawk's Pro Skater 2. That game was amazing when it came out. you've also got Legend of Mana Which is a sequel of sorts to Final Fantasy Adventure on Gameboy.
Both Oddworld games, Abe's Exodus and Abe's Oddysee are a must. Castlevania SoN , you had spot on. Those 3 games alone, are the only reason I still own ANY PS1 games. Parappa the Rapper, Um Jammer Lammy, and another game I kinda liked, was Star Wars: Masters of Tera Kasi. Pretty cool fighting game. The Spyro and Jet Moto series was pretty cool too.
You should definitely play Ape Escape. So fun. I also recommend Mr. Driller. Super addictive game. Also if you can find it pick up No One Can Stop Mr. Domino.
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Intelligent Qube, in my opinion, bridged the gap between Tetris and Lumines as far as puzzlers go
Sled Storm was a nice budget racer too
Bloody Roar 2
Final Fantasy 7
Final Fantasy 9
Legend Of Dragoon
Lunar
Lunar 2
Metal Gear Solid
Twisted Metal
Twisted Metal 2
Crash Series
Spyro Series
Army Men 3d
Blasto
There are a lot more, but I can't think of many at the moment.
Only ones i can think to add off the top of my head are Jet Moto 1 and 2 and Vigilante 8.