Downhill Domination (2003, PS2)
I loved this game. It was a great, adrenaline rush blast. It's downhill mountain biking where you can pick up power ups, including weapons, and you race to the bottom. A bit reminiscent of Road Rash in that you could punch your opponents off their bikes. The levels were pretty crazy, almost like Mario Kart, but the game provided you with a lot of freedom in how many lateral routes you could choose going down the races. Doing tricks gave you a bonus to your stamina. Playing two-player splitscreen was a lot of fun as well. I believe there was some customization for your bikes and upgrades for different things.
Amped 2 (2003, XBox)
The main appeal of this game, outside of being a 'realistic' snowboarding game which is about as rare a genre as you can find, was that the scores for your tricks weren't just judged on how crazy they were but rather how stylistically pleasing they were. For instance, sometimes doing a slower 360 with a grab would earn more points than a few backflips. It was a nice touch and a cool direction to take the genre in. Another odd yet charming part of the game was the online play. IIRC, you would just join a game and you'd be put onto a course with other people and that was it. No game modes. No formal start or ending to the game. In any other game, it would basically be a lobby for before the game starts. But then I thought of the snowboarding culture and how laid back everyone is, and realized this was some meta stuff. Really though, it's just because the online was probably an afterthought and they didn't put much time or effort in.
Blood (1997, PC)
A pretty over-the-top FPS game with ridiculous amounts of gore. Plenty of different weapons to choose from, the levels and map design were intricate and fun, and you could kick around people's heads after killing them so there's that.