Right off the top of my head, I'd say "The Seven-Ups" and "The French Connection" because they're great chases, and also noir classics, where there is no real redemption for any of the characters. The "winter in New York" settings for The Seven-Ups adds to the bleak mood.
While not a true chase scene, the bank heist scene from the original "Gun Crazy" with Peggy Cummins (oh, baby...) and John Dall is a classic now, but was far ahead of its time in the early '50s, shot in one take, from the back seat of the car. Love the way the tension builds, and the way Peggy works the wheel of the car (no power steering!), then the look on her face as they get away. If you've never seen this film you owe to yourself to see this masterpiece in its entirety!
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