Something I think the French Connection and Live in Die in L.A. chases have going for them that a lot of the more recent ones don't is a sense of real palpable danger. The protagonist isn't perfectly avoiding every hazard - they're just barely making it while endangering both themselves and everybody else on the road. Its messy, its desperate, and it many ways its a sign of how obsessed and possibly insane the participants are.
I really liked the Bourne movie car chases for a similar but different reason; they're kinetic. I don't think I've seen as many collisions instigated by the driver in chase scenes, much less situations where the car keeps on going after getting hammered a few times. I don't know how realistic it is that a tiny Euro auto can take that kind of a beating without killing everybody involved, but its almost like they took the intensity of their hand-to-hand fights and applied it to vehicular mayhem.
I don't know if anybody here has seen Dirty Larry and Crazy Mary, but its a '70s chase movie (there were a lot of those, really) which is a bit like Vanishing Point but loopier. Its another case of vehicles with possibly unstable people at the wheels doing amazing/terrible things, and the ending is pretty jaw-dropping.
Oh! And The Driver. Walter Hill movie with Ryan O'Neal as an honest-to-god professional getaway driver and Bruce Dern as the cop trying to catch him. O'Neal's character is kind of a cipher (common trait to Walter Hill heroes, really), but there's a long string of inventive cops-and-robbers chases that are worth seeing. If there was a film that actually featured a character who was as limited as the 2.0 Wheelman, it'd probably this one; dude doesn't do much other than drive.