Igor Stravinsky - Le Sacre du Printemps (Orchestre National de l'O.R.T.F, Pierre Boulez, 1963)
Ravel/Prokofiev - Klavierkonzert Nr. 3, Klavierkonzert G-Dur, Gaspard De La Nuit (Martha Argerich)
Frederic Chopin - Nocturnes (Rubinstein)
Gustav Mahler - Das Lied Von Der Erde (Otto Klemperer)
Johannes Brahms - Symphony No. 4 (Karlos Kleiber)
Sir Edward Elgar - Cello Concertos/ Sea pictures (Jacueline Du Pre, Sir Barbirolli)
Bela Bartok - Complete String Quartets (takacs quartet)
Erik Satie - Gymnopedies & other piano works (pascal roge)
Johan Sebastian Bach - 6 Cello Suites (Pierre Fournier)
Schumann, Piano Quartet Op.47/ Brahms, Piano Quartet Op.60 III Andante - Verbier Festival 2008 (Menahem Pressler, Salvatore Accardo, Antoine Tamestit and Gautier Capuçon)
Debussy and Ravel String Quartets (Alban Berg Quartett)

I also really like Debussy piano works and Beethoven's string quartets, but I don't have a favorite recording of those. This is also not the only classical I listen to, it's just the stuff that is indisputably classic to me.