Nice going Mark. First thread I've seen that mentions Peter Hammill, and an obscure old Genesis track like Snowbound. Not quite with you on the latter though - of the more romantic ones on that album I'd go for Undertow, or preferably Many Too Many - always one of my absolute favourites of theirs, and so overlooked. I did well up when they finished their 2007 reunion show with The Carpet Crawlers, Collins's touching intro to it - "We're finishing with this next one, which we think is what Genesis is all about".
I welled up last year watching Radiohead perform Reckoner. I have no idea what the song is even about, but something about the music and the plaintive vocal get to me.
I agree with two that have been mentioned - Lara's Theme, which was played at my Dad's funeral and was one of his favourite tunes (I'm getting emotional now just typing that), and Puff The Magic Dragon, which must be one of the most heart-rending evocations of growing up and the loss of childhood wonder.