The Bourne Identity chase with the Mini is one of my favourites. 20 years old now. 
when i think back to the golden age of car chases, if that's even a thing but yeah, a 70s thing, the only movies in 'recent memory' that reminded me of that level was the bourne movies
i do recall movies that had car chases in them of course, but chases that were exhillerating in and of themselves (eg it's literally the chase, not guns, not other shit, just the driving) is the shit i've said above - and i think it's a lot to do with the editing (or lack of) as much as anything else, i dont think many editors have that 'eye'
and im not really a fan of car chases, i can usually do without them, maybe that's why only a few catch my eye, which is probably telling in itself