This has always made me inexplicably happy, and it's my 12-year-old son's favorite as well:

http://www.youtube.com/watch?v=SnRm4Ipx8Eg

I also really like the Cupid Variation from Paquita. Here's a guy from the Trokaderoes performing it.

http://www.youtube.com/watch?v=4fd_bB3UXYw

And my favorite. I can't wait until my oldest daughter is ready to do this choreography, which her school uses:

http://www.youtube.com/watch?v=TaXQRJ2Om-A
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There are many favourites here, hard to single one out... I like Bach in general, how about Intermezzo from the Toccata in C:
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Wow... so many....
I love Vivaldi's "Four Seasons." Absolutely gorgeous.
"Moonlight Sonata" is great when you feel like lamenting or perhaps brooding over a particularly serious thought.
And of course, the Nutcracker Suite during Christmas. Good times....
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Beethoven's Fur Elise
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I can't say I'm capable of picking a single favorite classical piece.

There's something pure and wonderful about solo Bach. I particularly like the partitas for piano and also the sonatas and partitas for violin. This comes from my love of playing them. They involve great technique to play well and have such a complete sound. If you want to listen to something flashier this may not be for you but the second video of Glenn Gould playing is amazing! Much of my enjoyment of classical music pieces is from specific recordings so all YouTube videos posted are of older GREAT famous musicians and not random recordings.

For piano, I like the first partition in b flat. I really like the Praeludium:

http://www.youtube.com/watch?v=_0eTGdKliBM

The performances by Glenn Gould are enchanting. I love listening to him hum along. Here's a great video recording of him playing but not my favorite partita, Ouverture from Partita No.4:

http://www.youtube.com/watch?v=6nluYZFaaiA

I had to do another edit to add this. Bach's famous Chaconne - the last movement of the d minor partita for violin. Here's an Aaron Rosand recording. This isn't the best recording for sound quality but he's amazing and I've heard him play it live!

http://www.youtube.com/watch?v=YScAGFdWfeU

The recording of the Elgar Cello Concerto by Jacqueline Du Pré is incredible. Here's a link to the first movement:

http://www.youtube.com/watch?v=L5C99JyP2ns

I also love the Sibelius Violin Concerto. Here's a link to an old recording by David Oistrakh.

First movement:

http://www.youtube.com/watch?v=3SvAf-QbuvQ

Third movement:

http://www.youtube.com/watch?v=e5zy3oUZXGk

There are so many great composers... this doesn't even touch on any of the chamber music I love but it seems like time to stop posting more and more things :-)
Source(s):
YouTube

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SHEHERAZADE. by Rimski-Korssakoff so great in person if you get the chance to see an orchestra perform this one.
Source(s):
Youtube

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This is a great question but one I can not answer... I have tried and tried to narrow down to my one true "Favorite" piece and it doesn't seem possible. So, I am going to post a few pieces I could easily listen to/play over and over again!

Bolero - Ravel:
http://www.youtube.com/watch?v=v1x3QoibhlY

The Planets - Holst:
http://www.youtube.com/watch?v=L0bcRCCg01I
http://www.youtube.com/watch?v=oKvG0RU4_fI
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It would have to be Moonlight Sonata by Beethoven.
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If I had to pick a single favorite, right now it's The Lark Acending...

Part 1:

http://www.youtube.com/watch?v=oz1hWcPkods

Part 2:

http://www.youtube.com/watch?v=2sjsVE-AznM

It's evocative of pure timeless beauty, but also an elegaic remembrance of a lost world. Very simple, but somehow piercing and moving too.
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