In no particular order...
Flashback (Sometimes subtitled as Quest for Identity):
It had really smooth animation and the shooting was nice and punchy. Firefights could be over in two seconds, but you had to plan your movements and shots precisely. Well, until about halfway through when the enemies changed and then everything got shitty and repetitive.
The Exile series (Escape from the Pit, Crystal Souls and Ruined World. Later remade as the Avernum series.):
My first RPG. Kinda crappy in hindsight, but the setting was legitimately unique (an underground fantasy prison colony) and I got quite absorbed.
Giants: Citizen Kabuto:
It let you play as a crew of space pixies with heavy weapons and jetpacks, then a topless alien witch, and then a giant. The witch could summon a proper legit fucking tornado. The giant could eat enemies and make earthquakes with his attacks. Do I even need to explain why this made an impression on a kid? It was also the first game where I got into the online multiplayer, but I got my arse kicked because I was on Australian dial-up and the only populated servers were in the US. I didn't know about latency back then, I just thought by aim was terrible.
Oni:
Third person beat-em-up with a bit of gunplay on the side that was desperately trying to be Ghost in the Shell. Had really sweet combat. There was a move where you grab a guy by the neck and swing yourself around him, kicking anyone else in range. There were disarm moves where if you used them while you where unarmed you would end up holding the weapon ready to fire and the whole transition was buttery smooth. There was a stun move that amounted to kicking enemies in the crotch and didn't work on female enemies (I spent hours testing that, bitches kept dodging.) I also rather liked the story, although in retrospect it was rubbish.
Halo: Combat Evolved:
Oh, fucking sue me. That multiplayer was a barrel of fun. Back in the day I could make goddamn magic happen in one of those ghost hover bikes.