I agree about Chicago's "Look Away"...good song from back in the day when America still made good music. And it perfectly describes how a breakup should go--the line "when we both agreed as lovers we were better off as friends"--too bad that doesn't seem to happen all that often with some people anymore. (I am on good terms with all of my exes for some reason...plus I've been single for almost four years now).
And as for regretting it, try ATB's "Let U Go" (either the 2001 or 2005 version, they have the same lyrics). I like to think of this song as not only a breakup, but also perhaps as a missed opportunity. I think back to April 4, 2005...a day I was going to ask a girl I liked to prom but never got around to it because I got held up in English class. I missed the deadline to ask someone as a result of this. I always think of what could have come from this--we had so much in common and were probably the only two people who thought the same in the school--but in the long run I realize we're probably better off as friends because I don't think either of us would ever want our friendship to end!
But anyway, that song is a suggesstion if you interpret it differently.