I can't name the three *most* affecting: that various depending on my mood and a host of other circumstances. But here are a few very random pieces that came to mind as very moving:
Beethoven's 5th, 6th, 7th symphonies
Bach's Goldberg variations
Mozart's Piano Concertos 23, 21
Bizet's Carmen and Le Arlessienne Suites
Rachmaninov's 3rd piano concerto
Tchaikovsky's violin concerto, symphonies 4-6
Mendelssohn violin concerto, Italian symphony, octet
Schubert trout quintet
Brahms Hungarian Dances
Haydn Symphony No. 94
Bach solo cello suites
Strauss waltzes
Bolling Suites for Flute and Jazz Piano
Mussorgsky's Night on a Bald Mountain
A smattering of my perhaps "cheesier" choices ;-) :
"Meeskite" from the musical Cabaret
Butterfly Kisses by Bob Carlisle
Bohemian Rhapsody by Queen