Ah yes, Donnie Darko is great.
If you like the themes/narrative technique of Donnie Darko, then check out:
David Lynch films (Mulholland Drive, Blue Velvet, Lost Highway, Wild at Heart).
I would say Donnie Darko is very much like Lynch films.
Also, Michaelangelo Antonioni's "Blow-Up" is a great choice for films presented in a surprisingly new way. Peter Weir's "Picnic at Hanging Rock" is another one.
There are a million other great films that I'm sure you would love (Memento, Fight Club, Requiem for a Dream, etc etc)--but the ones I mentioned above (Lynch, Antonioni, Weir) are the most akin to Donnie Darko (or rather DD is akin to them)
Enjoy watching these great films...I envy you...getting see all these great films for the first time :)
Trevor