"Daddy, What If?" by Shel Silverstein [recorded by Bobby Bare]

"Little Child (Daddy Dear)" sung by Cab and Lael Calloway

"Something Wonderful" from "The King and I" -- sung by the king's no. 1 wife, but just as applicable to fathers

And for funny songs, there's "Father's Whiskers"

Also, in a lighter vein, when I do Father's Day programs, I like to throw in "My Heart Belongs to Daddy" and "Papa, Won't You Dance with Me" and "I’m My Own Grandpa."