I try to play music before my classes start. Here's some of my favorite music.
For details of the music and their composers/performers, I highly recommend: http://www.grovemusic.com/index.html. For reviews of classical recordings, I use http://www.gramophone.co.uk.
Johann Sebastian Bach: St. Matthew Passion; Passacaglia and Fugue in c minor (organ); O Mensch, bewein' dein' Sünde gross (organ)
Bela Bartok: String Quartets #5 & 6; Music for Strings, Percussion, and Celesta
Ludwig van Beethoven: Grosse Fuge; String Quartets No. 14 & 16; Symphony No. 9
Alban Berg: Wozzeck; Violinkonzert
Luciano Berio: Sinfonia
Benjamin Britten: Peter Grimes
John Cage: First, Second & Third Construction
John Coltrane: A Love Supreme; Naima (from Giant Steps)
Aaron Copland: Quiet City; Midday Thoughts (piano)
Miles Davis: Kind of Blue; 1964 Complete Concert; Bitches Brew
Guillaume Dufay: Hymns
Maurice Duruflé: Prélude, Adagio et Choral Varié (organ)
Duke Ellington: Black, Brown and Beige
Bill Evans: Conversations with Myself; Live at the Montreux Jazz Festival; Portrait in Jazz; Since We Met
Charles Ives: The Unanswered Question; Variations on "America" (organ)
Olivier Messien: Turangalila Symphonie; Quatuor pour le Fin du Temps
Charles Mingus: Mingus Ah Um
Wolfgang Mozart: String Quintet #4 in g minor
Conlon Nancarrow: Studies for Player Piano
Arvo Pärt: Tabula Rasa; Fratres; Trivium (organ)
Steve Reich: Come Out; Music for Eighteen Musicians; Different Trains; City Life
Igor Stravinsky: La Sacre du Printemps; Agon
Ralph Vaughn Williams: Five Mystical Songs
Other musicians I like: Radiohead, Bob Dylan, R.E.M., The Smiths, The Shins, The Police, Wilco, Nick Drake, Bob Marley & The Wailers, Deathcab for Cutie, The Clash, Counting Crows