Honeysuckle Rose, by Django Reinheirt
It Had to be You, by Harry Connick, Jr.
Time after Time, by Frank Sinatra
(This is a little too slow for my tastes, but the Chet Baker and the Harry Connick Jr. ones are much less dancable)
And saving the best for last:
All of Me, by Count Basie and his orchestra
(The Sinatra at the Sands concert has a recording of this, fyi.)
What was your first dance? And what was your Father-Daughter dance? (My own father would insist on a waltz, which is awesome.)