Is the song in 3/4 time? If it is, you can waltz to it. If you can't recognize the rhythm then you will have a tough time dancing any dance to any song.

"Slow Dance" - Michael Peterson
"Put Your Dreams Away" - Frank Sinatra
"I Will Love You" - Fisher
"Sleepsong" - Secret Garden
"Since You Asked" - Natalie Cole
"The Old House" - Phil Coulter (piano)
"Thr Green Fields of France" - Phil Coulter (piano)
"Natasha" - Phil Coulter (piano and not strict tempo)
"May Each Day" - Andy Williams
"Remember" - Andy Williams
"Illusion" - Nat King Cole
"At This Moment" - Michael Buble'

I don't think anyone else has mentioned any of these, and some are among my all-time favorites. My wife insisted on "Slow Dance" for our wedding song. (I would have preferred "Since You Asked")

"With you I'm born again" by Billy Preston.

Great thread! I appreciate the suggestions for a greater variety of dance music.

I was surprised not to see this one: Cait Agus Sean - Flying

A great V walz and modern.... Blackheart (2 steps from hell)

Great suggestion! I'm going to teach a waltz line dance to this one!

Mull of kintyre paul mccartney Has a very strong 3/4 time easy to dance to

Pretty Paper Roy Orbison
How do you start over Roy Orbison
To soon to Know Roy Orbison

Only love can break you heart - Neil Young
Waltz number 2 - Eliot Smith
The day the courasel burned down- Todd Rundgren

They are a bit old, but I like these:
Kenny Rogers - If I Were a Painting
Andy Williams - My Coloring Book
Andy Williams - Charade
Goya Matsuda - Moving On
J Johnny Mathis - Foolish
Tom Jones - Funny Familiar Forgotten Feeling
Dinah Washington - Fly Me To The Moon
Until It's Time For You To Go - Don't know the artist