Let's go for a classic George Harrison/Beatles' song. "Something in the Way She Moves." It's slow; it's romantic; it's plantive; and it mixes it up enough, so that it is not predictably cheesy.
My favorite slow song of all time is David Gray's "Be Mine." I used it as my entrance song for my wedding instead of the traditional music. I also like Ben Folds' "The Luckiest."
Generally, I think I end up liking music that has honesty in the message and is very personal, but not cliche and cheesy. Both of these songs fit that description. Every once in a while there will be a slow song on the radio that I like the first time I hear it (like Christina Aguilera's "You are Beautiful") but then it gets so overplayed that I find myself hating it.
I have quite a few... on the top of my head, I can say, Prince 'International Lover,' All-4-One 'I Swear,' Boyz II Men 'End Of The Road' and 'Dear God,' Celine Dion and R Kelly 'I'm Your Angel,' The Commodores 'Easy,' Freddie Jackson 'Rock Me Tonight,' John Hiatt 'Straight To The Heart Of Love,' Lionel Richie 'Stuck On You,' Prince 'Nothing Compares 2 U,' Prince 'The Most Beautiful Girl In The World,' and Prince 'The Beautiful Ones.'
Thanks for your question!