My favourite chase movie of all time: Thelma and Louise. It doesn't get much more pure than that one. And, it's interesting in that they never do reach their initial goal, to escape over the border into Mexico. The twists and turns in this one are less in the chasing/eluding than in the realizations the characters make along the way.

BULLITT. Classic cop drama from 1968 starring Steve McQueen as San Francisco Police Detective Frank Bullitt. This film set the bar very high for every car chase movie since. Unlike some films that seem to be in 'chase mode' from the get-go, Bullitt had a specific chase scent in the movie that was some 10 minutes long. The BULLITT car chase through the legendary streets of San Francisco to the outskirts of the city featured McQueen (a competitive Car & Motorcycle racer in his day) behind the wheel doing all of his own high speed driving. It was produced by McQueen himself (Solar Productions), directed by Peter Yates, with a screenplay by Alan R. Trustman & Harry Kleiner. Because of it’s sparse, tight dialogue, great supporting cast and of course, Steve McQueen... it still plays well today..., some 45 years later.

Thelma & Louise is a classic chase movie. And you're right, there is a powerful internal journey the two central characters go through to match up to their external adventure.

Kevin, I'm glad you mentioned Bullitt because it IS a classic. Also happens to have one of the greatest car chases in cinema history.