Gone in 60 Seconds. (the remake) Nicholas Cage did all the driving except for the jump (and most of that was CGI anyway).
Also Torque. Really bad movie about Super Sport motorcycles, but near the end there is a car chase in which the FBI chases them in a NASCAR. Dont ask how he got it but yea. Also in the end of that movie there is a bike chase on the Y2K bike (jet engine powered super sport) kinda neat but a lot of CGI as well.
Actually, it's been said later that Cage did not do it but there was a steeringwheel to the backseat. I also did wonder since in the start of the chase where he does a 180 to avoid the cops, he doesn't steer as much (or at all) when the car moves, and throttle and brake control couldn't do that.
The car that physically jumped up and landed had 800lb/in springs and as you can see, it still smashed the suspension (it's in the trailer that's on the DVD that shows more than the swerve after the landing, the frontwheels had extreme camber so I suspect the frame/links got bent and it actually oversteered and hit the wall but the scene was cut before that for the movie).
Also, the car in the movie was supposed to be a GT500 but were just normal 67-68 Mustang fastbacks. Several people call the movie-car GT500E but that's the name of a limited edition model made after it, except it had different instruments and a ugly raised bump on the nose. The real Eleanor in the movie had normal instruments but a racing tachometer on the steeringcoloumn, the production GT500E has all-white aftermarket instruments mounted in the dash.
The moviecar, or some of them for stuntwork at least, had rack-and-pinion steering with a new power-steering system allowing much more precise steering and coilover suspension and GoodYear F1 245/40-17 tires. The high-speed model used a Ford motorsport V8 with 400hp. Some of the cars had automatic transmission, possibly for use for Cage for filming his face when driving past the camera.
They did plan on really speeding in the flood control, but it had been flodded when they arrived so it physically wasn't possible to drive that fast, therefore they undercranked the camera. That's the scene btw with the A-Star doing some seriously low flying. In that scene however I hate that he pushed the nitrous oxide button when the tachometer reads 7000+ rpm, that would surely smash even a sturdy US V8 engine, not to mention that the increased power had to be able to be transferred to the ground by the tires.
Oh yeah, one more detail, when he starts Eleanor, it's not a Ford starter engine. When he drives across the road where the cruiser gets hit by a bus, you can see a key in the ignition. When he restarts the car after it stalled after loosing the cops in the flood control, he only uses one hand, where he used two hands to operate the two picks in the garage.
A real fast carchase could be in the french movie Taxi (the one that the US version was a remake of, that even Queen Latifah and Jimmy Fallon couldn't make funny, and that btw did have CG effects). The Peugeot 406 stuntcars were driven by famous french rally and stunt drivers and actually did drive pretty fast, not sped-up filming. Evidence indicates that one of the scenes actually used a 406 Touringcar (racecar) since a rollcage and a very low seated driver could be seen in shadow thrue some heavily tinted windows.
Frank