Here are my recommendations. I don't sing them but they remind me of the characters.
The Mortal Instruments series - Jace and Clary
Can You Hear Me - Poets of the Fall
(I don't know why, but whenever I hear that song, I think about Jace and Clary)
The Twilight series - Bella and Edward
All the way/4U - Poets of the Fall
(This song could belong to so many pairs that I have lost count. However, when I was told that it was supposed to be used in Twilight, but was later removed, I always think of them when I hear it.)
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Sing Me To Sleep - Derek and Beth
Cradled in Love - Poets of the Fall
(This one was a tough choice between 'A Walk To Remember' by Nicholas Sparks and 'Sing Me To Sleep' by Angela Morrison but I felt 'Sing Me To Sleep' was more suitable.)