I got most of these; If you're playing along at home:
Attempt 1: Clair de Lune (Claude Debussy)
Attempt 2: ??
Attempt 3: Moonlight Sonata 3rd Movement (Beethoven)
Attempt 4: Harry Potter theme (John Williams)
Attempt 5: Pokemon theme (John Siegler)
Attempt 6: Flight of the Bumblebee (Nikolai Rimsky-Korsakov)
Attempt 7: ??
Attempt 8: Russian National Anthem (Alexander Alexandrov)
Attempt 9: Get Along Gang theme (don't know who wrote this)
Attempt 10: Blue (Eiffel 65)
Attempt 11: Thomas the Tank Engine theme (Mike O'Donnell/Junior Campbell)
Attempt 12: Funeral March (Chopin) I'd be surprised/alarmed if she smiled at this (!)
Attempt 13: Jaws theme (Williams)
Attempt 14: Halloween theme (John Carpenter) this too (!)
And the winner..well, you know, a chick song from a chick movie, no wonder she smiles...

Tags for this video have been changed from 'piano, solo, animation' to 'piano, solo, animation, claude debussy' - edited by Issykitty

It's Claude Debussy's Nocturnes: Sirènes
*bravo

>> ^Bradaphraser:

I must know what this music is! It's dreamy!

Tags for this video have been changed from 'jean pierre rampal, rampal, flute, claude debussy, debussy, syrinx' to 'jean pierre rampal, rampal, flute, claude debussy, debussy, syrinx, 1957' - edited by Deano

"Allegro non troppo is a Bruno Bozzetto animated film released in 1977. The film is a parody of Disney's Fantasia, though possibly more of a challenge to Fantasia than parody status would imply. In music, an instruction of "allegro ma non troppo" means to play "fast, but not overly so". In the context of this film, and without the "ma", it means Not So Fast!, an interjection meaning "slow down" or "think before you act" and refers to the film's pessimistic view of Western progress (as opposed to the optimism of Disney's original).

The film features six classical pieces:

Prélude à l'après-midi d'un faune by Claude Debussy
Slavonic Dance No. 7 by Antonín Dvořák
Boléro by Maurice Ravel
Valse Triste by Jean Sibelius
Concerto in C Major by Antonio Vivaldi
The Firebird by Igor Stravinsky

The classical pieces are set to color animation, ranging from comedy to deep tragedy. At the beginning, in between the animation, and at the end is black and white live action film, displaying the (well, not the actual) animator, orchestra, conductor, and filmmaker, with many humorous scenes about the (again, not actual) production of the film."

/ Wikipedia link

Finally, additional props to sometimes for posting the sad cat segment of this intriguing movie.