F Zero GX.

The insane sense of speed, the silky 60fps, the brutal difficulty, the perfect blending of Sega punk-rock attitude with Nintendo polish, a true gem.

Project Gotham Racing 4

I cant just pick 1. so I will pick one for the 3 categories
Arcade- Diddy Kong Racing
Sim- Gran Turismo 4
Street- NFS Most Wanted

1. Need For Speed: Hot Pursuit 2. (clear winner too, awesome racing, awesome soundtrack)
2. Rage Racer.
3. SEGA Rally Championship: 1995.
4. Sonic & All Stars Racing: Transformed.
5. Burnout 3
6. Metropolis Street Racer.
7. Gran Turismo 3.
8. Ridge Racer Type 4.
9. Forza Motorsport 3.
10. Burnout Revenge.

Colin McRae Rally, on the PS2.

For me, it is a tie between Mario Kart Wii and Diddy Kong Racing.

I see six people already said Diddy Kong Racing before me. They must have very good taste.

It's a toss-up between Mario Kart 64, Cruis'n World, Wave Race and Need for Speed 2.

Excite Truck and Extreme G (the first one...the good one) are honorable mentions as well. And for some reason I really kinda liked the Indy 500 arcade racer.

This is the most memorable and all time favorite racing game.

I played the hell out of this game when I was a kid. A more recent game would be: 

Kart - Crash Team Racing
Arcade - Driver San Francisco
Sim - Gran Turismo 5

A few votes for Need For Speed: Hot Pursuit 2. (those who aint played it, get your ps2 out of retirement and buy that masterpiece NOW..!!!)

Would love that game on xbla/psn etc.