Thank you, Groucho. The Adagio is the one and it is beautiful. Isn't technology wonderful?
The link instantly played the whole thing! I will have to research Barber, I never heard of him before.
I thought of a few more possible tear inducers:
The Way We Were (Redford, Streisand and the song Memories...)
Love Story (O'Neal, McGraw, and another iconic sad song)
Sounder
Rocky