Another "Muppets" fan, here! I love "Somebody's Getting Married!" I woke up with that song in my head the morning of my wedding. I thought about using the song, but it didn't fit in the ceremony anywhere. I also thought about using "He'll Make Me Happy." It's the song Kermit and Piggy sing to each other at their wedding.
My dad took me to see The Muppet Movie when it first came out. I was around six. I remember feeling so special because it was just my dad and me, so I used "Rainbow Connection" for my Daddy/Daughter dance.
DH and I used Pete Townshend's "Let My Love Open the Door" as our first dance song. It was the slower, longer version, not the version used in the Adam Sandler movie, Mr. Deeds.