I've been to many a wedding with a father/daughter and mother/son dance-- it's very touching, but let's be honest... nobody wants to sit around and watch the bride have a cheesy moment with her father while being forced to listen to "Butterfly Kisses" by Bob Carlisle for the billionth time. Also, let's be honest, a song that my father and I always liked was "Behind Blue Eyes" by The Who and that is SO not a wedding song or even one that anyone else would understand.
Instead, how about a father's toast? Everyone likes a toast at a wedding, it means you get to take one more swig of champagne, and most fathers don't tend to get a chance to say how they feel about the couple and the journey they're about to go on in life. Yeah, OK, so a toast isn't a novel thought, but I'm also willing to bet that most dads out there are a little more excited about public speaking than public dancing!
If you happen to be in the position of not having your father with you and you have notice, set up a small remembrance table or a series of pictures of you and your father-- the you here can refer to bride or groom, as frequently the groom's father isn't really mentioned. I'm a big fan of the pictures at receptions trend, so there will be more on that later.
Happy Father's Day!