Time Travel/Loop or Alternate Reality Movies

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Run Lola Run: Turns the, "Time Travel," trope on its head. Great little German film.
Dark City: Dystopian and weird, but an awesome film. Alex Proyas is a great director.
Non ci Resta, Che Il Crimine (erroneously translated as All You Need is Crime): A fun Italian film with a bunch of big name, MODERN Italian actors, they are soccer fans who get transported to 1982, during the World Cup.
Il Capitale Umano: Another great Italian film, it was remade in 2019 starring Liev Schreiber. This film has the first half or so, flashback 3 times, each in the POV of someone different, so not quite time travel, but switching back and forth.
Swimming Pool: French film that plays with your head in many ways; NOT a time travel film, but absolutely an alternate reality film. One of my favourite film lines ever came from this, a play on the, "every asshole," line: "Awards are like hemorrhoids; eventually, every asshole gets one."

And it's been mentioned, but Donnie Darko is just fantastic, a truly deep film.