Favorite Racing Games With Weapons

Racing, not car combat (ie no Twisted Metal, Vigilante 8, etc)

My picks
Super Mario Kart (SNES)
Diddy Kong Racing (N64)
Snowboard Kids 2 (N64)
Extreme-G (N64)
Mario Kart Double Dash (GC)
Rock N' Roll Racing (SNES) 

CTR

Sonic & All-Stars Racing Transformed (PC/360)
Cyber Speedway (Saturn)
Dethkarz (PC)

A general order:

1. N-Gen Racing (PS1)
2. Mashed: Fully Loaded (PS2)
3. Re-Volt (PC)
4. Extreme-G 3 (PS2)
5. Grooverider (PS2)
6. Slipstream 5000 (PC)

Still going with Mario Kart.  Any of them.

Mario Kart (any)
Crash Tag Team Racing (PSP/PS2)
Little Big Planet Karting (PS3/PSV)
Modnation Racers (PS3/PSP)
Crash Nitro Kart (PSX) 

Road Wars (PC)

It's not legacy, but WipEout HD Fury is the best racing game that I've played, period.