Lots of great suggestions, I'll remove my duplicates.
- Rollcage Stage 1 or Stage 2
- Star Wars Episode I Racer
- Lightbikes (Eidolon Industries)
The beauty of old LAN gaming was the modding scene.
Some of my favourites:
- Quake 1 = Quake Rally, Demolition, Painkeep, Action Quake
- Quake 2 = Powerball, Devastator,
- Quake 3 = CrateDM, Corkscrew, Superheroes, Proball
- UT = Excessive, Invasion
Demolition was awesome - it was single-goal (team) deathmatch where the ball was a bomb on a timer with a vast blast radius. Score before it exploded, or rack up kills with it instead of scoring.
CrateDM was great - your player model was a crate, the map was a warehouse full of crates. Sneaky tactics for a last-man-standing game mode.
Proball - feels like a 15 year predecessor to Rocket League!
Excessive - this was what made UT as insanely fast as Q3A. It always felt like the movement and damage was insufficient in UT, and the Excessive mod dialled everything
up to 11.