I remember now! It was Rollcage (and the sequel, Rollcage: Stage II) by Psygnosis. They came out for the PC and PS1.
Man, Psygnosis was a GREAT developer.
Yup. Rollcage II was released in the states as "Death Track Racing".
It is worth noting that Psygnosis was not the developer, ATD was (Psygnosis might have been the publisher).
ATD later did LEGO Drome Racers, which is very much a spiritual sequel to the Rollcage series, though I miss some of the neat play modes (esp from RII).
I'll also add a hearty thumbs up for Trackmania (only played demo for Sunrise, but looks great). Great choice, unless you're one of those folks who gets all wigged out about Starforce.