What are your top three favorite classical compositions?

Three!? Seriously!

I could never narrow it down to just three, even 10 wouldn't be able to cover all the classical music I rate equally highly. So, I will have to cheat. 😉

I am only into: 20th century, atonal, serial, avant-garde classical music. Mostly from post 1950 to the present.

Alban Berg - Violin Concerto 

Elliott Carter - Concerto for Orchestra 

Charles Wuorinen  - 4th piano Concerto 

Joan Tower  - Concerto for Orchestra 

Ernst Krenek - Static and Ecstatic 

Magnus Lindberg  - Sculpture

And a few, less 'thorny' sounding pieces:

Bartok - Music for strings, percussion, celesta

Samuel Barber - Piano Concerto 

Stravinsky - The Rite of Spring 

Again, there are many other pieces that I rate as highly as those I listed. If I made this list tomorrow, it could be almost completely different. 

As it appears most folks like orchestral,

 

My list is mostly orchestral, only because those are the pieces that come to mind first.

But truth be told, there are plenty of pieces for chamber ensembles that I rate equally as those in my list above.

Charles Wuorinen - Chamber Concerto for Oboe and 10 Players (1965), Chamber Concerto for Flute and 10 Players (1964)

Elliott Carter - String Quartet No. 3 (1971), and No. 2 (1959), Asko Concerto for sixteen players (2000)

Anna Thorvaldsdottir - Hrim (2010),

Stravinsky - The Soldier’s Tale (1918)

Stefan Wolpe - Chamber Piece No. 1, chamber orchestra (1964)

Magnus Lindberg - Souvenir (2010)

This is exactly why the OP’s request for only 3 pieces is an impossibility.