It's nice, of course, if the song is special to the couple. But honestly, I think even more important is that the song be short -- it's amazing how long even thirty seconds will seem; stand still and count and you'll see -- and easy to dance to. That's one of the reasons old standards like "The Way You Look Tonight" and "At Last" are popular choices.
In my experience, the Special Dances (first dance, father daughter) work best when others (bridal party, parents, siblings) join in along the way.