Best movie similar to Donnie Darko (2001)

Primer (2004). "The permutations were endless."

I strongly agree that 12 Monkeys (1995) is similar.

Brick (2005) for the setting.

A Scanner Darkly (2006) for the mood.

Best I'd say is 12 Monkeys, but that's unsurprisingly already been mentioned.

An odd one I want to recommend - Static (1985) - IMDb link

It's broadly similar in that it's surreal and unsettling and deals with alienation, loneliness and death, and it has a great soundtrack (and in fact introduced me to The The's This is the Day, almost 40 years before GotG v3). And it stars Keith Gordon and Amanda Plummer, who are both excellent.

The most notable difference (not so much that it's vital as that it's so obvious) is that it looks completely different. Visually, Donnie Darko is very dense and rich and dark, while Static is very pale and washed out and stark. It fits the context though.

Jacob's Ladder

12 Monkeys

Fight Club, even ends with a good credits song

Maybe Stranger Than Fiction? Not quite as dark but a story about a simple change in a man’s life with a huge impact on the rest of it. It is a Will Ferrell flick but not your typical experience from him.

The Wave with Justin Long could maybe scratch that itch too.

Let the right one in (2008)

My recommendation is:
Enter the Void (2009)
The movies explores topics of the afterlife, the nature of consciousness, and the interconnectedness of life and death. I am quite fond of the neon-soaked psychedelic visuals.