What are your top three favorite classical compositions?

As it appears most folks like orchestral, a few that are heard more often in my house - Sibelius Sym #4 (and his Finlandia Hymn, original version, by male choir, highly recommended for those who feast on nationalistic music), Last movement of Mahler's #2, all of Mahler #6, Prokofiev's Piano Concerto #3.

Another three off the bottom of my head --

Mahler's Wunderhorn songs.

Stravinsky's Petrushka

Puccini's Turandot.

A great question.  For right now, I'd have to say:

--Beethoven's Ninth Symphony.

--Mahler's Second (Resurrection) Symphony

--Mozart's Don Giovanni

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.

Not so deep into classical but 3 (even...3) is impossible, i will follow the rules,

Berlioz Symphonie Fantastique

Britten The Young person’s guide to the orchestra

J.S.Bach The concertos for 3 and 4 Harpsichords (BWV 1065, 1064, 1063)

First ones most likely they come from my childhood.