Ok, I know that this isn't the ONLY other song I have on my personal Twilight playlist, but here's one that always makes me think of Twilight."Before It's Too Late" by the Goo Goo Dolls
I know that they wrote it for the couple in the Transformers movie, BUT every time I heard it last Fall (while reading Twilight for the first time), it totally fit Edward and Bella.
This is the Twilight theme song, for me anyway! "Her Eyes" by Pat Monahan
(not all the lyrics, but more of the melody i guess)