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1.
Occurs during doggie-style sex when the man is thrusting vigorously into the woman's vagina, then abruptly pulls out and jabs his penis in her anus. The "curb" in this case is the woman's perenium (or "taint"). If the woman complains, the mans feigns innocence and claims it was an accident.
Last night my old lady said she didn't want anal, so I just jumped the curb.

If you jump the curb enough, your girlfriend will figure out you're doing it intentionally.
by Big J-Loc November 20, 2005
 
2.
The act of literally jumping a car over a curb, usually done under one of two instances:

1. A drunk driver wiping out

or

2. Someone is intending to hit someone

The second condition happens more in video games than in real life, and the phrase was often heard back in the mid-90's by players of Twisted Metal. It can be heard more now by GTA players, as the shouting of "jump the curb!" at the player is an encouragement to run over pedestrians.
1. The drunk man tried to flee to cops, only to jump the curb.

2. "Hit 'em, hit 'em! Jump the curb! Smash!!!"
by ObscuredOne November 24, 2006