The Luckiest by Ben Folds.
Of course, we divorced after 5 years of “bliss,” so I guess I got even luckier.
Ice Cream by Sarah McLachlan
It made a nice waltz
Keith Whitley’s ‘When You Say Nothing At All.’
A cover of the Beach Boys’ “God Only Knows” by Holly Cole.
“Lean On Me”
We had a small band at our wedding in 1987, and we mostly had them play Motown hits, figuring those would bridge the generations pretty well.
Heavenly DayPatty Griffin
Oh, thanks for dredging up an awful memory! 
Let me first say that I did not want a wedding ceremony, and second, I don’t dance. However, my husband-to-be and my mother and my grandma and everyone else seemed to have their heart set on seeing me walk down an aisle in a white dress so that’s what happened. Husband-to-be let me choose the song. (I really wanted Weird Al’s Good Enough for Now, but knew it would not go over well.) So anyway, I chose Sting’s *Fields of Gold because although my husband and I have very different musical tastes, it was a slow song we could both at least tolerate.
So, the big day comes, and it was nice but also stressful. I’m doing my damndest to get properly married and then the time came for us to dance with everyone looking at us. So we began shuffling around the dance floor. About a year later, we were still shuffling, the music was still playing, and I could not stand being looked at one more minute. So I dragged new husband off the floor and we sat down. The DJ and everyone else was totally confused. After a while, *Fields of Gold *ended and something else was played and people shrugged and the wedding ground onward. Ugh!
*god, I hope I never hear it again.
All the Things You Are - Ella Fitzgerald. 
Also eloped and got married alone. We aren’t really Show People.
We allowed both sets of parents to throw reception parties for us, though, so they could show us off to their friends and invite the relatives. Also because it was their only chance to throw wedding parties, because our siblings are even less traditional than we were.
Ukulele Lady’s Mom threw theirs in their new house in Chicago, and did the catering herself (she’s Greek, and does excellent Greek food). Don’t remember any music there.
My father owned stock in a golf/marina resort on Lake Erie, just east of Sandusky, so he did it there, and made everyone schlep out from Cleveland.
He asked what kind of live music we wanted, so I asked for a small swing group to do Ellingtonia and other early 20th century jazz standards. He found a very nice Nat King Cole-style trio of piano, guitar, and bass, just what we wanted. But I don’t remember anyone dancing. Must’ve been the open bar.
Several Old People there asked me why we wanted Old People Music. I should’ve brought my Grateful Dead bootlegs and treated everyone to 45-minute “Dark Star” jams.
“Reminiscing” by Little River Band
Book of Love - Peter Gabriel
We both love the TV show Scrubs. And we are rubbish dancers, so better to just move around slowly. We were also both quite drunk by that point.
Michael Buble - Feeling Good
A friend of ours got married to a guy who’s a tie-dyed-in-the-wool Deadhead; the one thing he insisted on for the reception was that their first dance would be to a Grateful Dead song. She didn’t know enough about the Dead to ask how long the song was…apparently, it was a 7-minute song, and she felt like it was the longest 7 minutes of her life.
I’ve actually been to a wedding where “One More Minute” by Weird Al was the first dance song, and another one where “Masochism Tango” by Tom Lehrer was it.
“Bess, You Is My Woman Now”, as performed by Ella Fitzgerald and Louis Armstrong.
In retrospect, that may have not been in the best taste, as neither of us is African-American - but it was written by two Jewish white guys, so that counts for something, yes?
The point was, the song spoke to me - I’m the one who always had commitment issues, which most folk who were there knew about, so it was my way of saying that I was absolutely making this commitment with all of my heart.
It was supposed to be “Unforgettable” by Nat King Cole. We thought the DJ was going to bring it, he thought we were going to bring it. We quickly settled on, uh… let me look it up…
“Keeper of the Stars” by Tracy Byrd. I think. I wasn’t all that important. We thought of it as the “one thing that goes wrong” at a wedding.
Grow Old with You by Adam Sandler
My wife and I have opposite tastes in music and we couldn’t agree on anything. I suggested it as a joke but she thought the sentiment was sweet and liked the movie. The next thing we were out there dancing to it to much laughter.
Ok…first wedding, the huge Catholic extravaganza back in '91, Sea of Love by the Honeydrippers
second wedding, smaller, family focused- Truly, Madly, Deeply by some Australian group…forgot who they are
And last wedding…I don’t think we danced. We eloped and got married barefoot at sunset where I burst into tears, because deep down, dammit, I didn’t want to get married again, but there I was…lololol
Didn’t have dancing at our wedding but from my memories of the playlist we put together on the iPod it could well have been *Cows With Guns * by Dana Lyons, one of the songs from *Dr. Horrible’s Sing-Along Blog * or something from *The Commitments *soundtrack.
I honestly don’t remember.