We had Ben Harper, By my Side, and there is another song of his that I can never remember the name of that is great too - my BIL had it at his wedding....if I can think of it will post again... I would just choose a nice song that reflects who you both are rather than it being a 'wedding" song if that makes sense! All our music was like that throughout the day with music we just loved, so we had Dave Matthews band while signing the register, Coldplay as we walked out and the Corrs when we walked in!
Good luck!!