Hors concours (1):
Johann Sebastian Bach
The immortals (3):
Johannes Brahms, Gustav Mahler, Franz Schubert
The geniuses (9):
Claude Debussy, Antonin Dvorak, Felix Mendelssohn, Ernest John Moeran, Wolfgang Amadeus Mozart, Maurice Ravel, Dmitri Shostakovitch, Jean Sibelius, Richard Wagner
The grandmasters (27):
William Alwyn, Samuel Barber, Arnold Bax, Ludwig van Beethoven, Hector Berlioz, Benjamin Britten, Anton Bruckner, Frederic Chopin, Gabriel Faure, Edvard Grieg, Sofia Gubaidulina, Joseph Haydn, Modest Mussorgsky, Carl Nielsen, Sergei Prokofiev, Giacomo Puccini, Joachim Raff, Einojuhani Rautavaara, Ottorino Respighi, Camille Saint-Saens, Aulis Sallinen, Richard Strauss, Josef Suk, Toru Takemitsu, Pyotr Ilyich Tchaikovsky, Peteris Vasks, Ralph Vaughan Williams
The masters (81):
John Adams, Kalevi Aho, Hugo Alfven, Anton Arensky, Malcolm Arnold, Kurt Atterberg, Grazina Bacewicz, Carl P.E. Bach, Granville Bantock, Amy Beach, Alban Berg, Luciano Berio, Max Bruch, Gavin Bryars, John Cage, Aaron Copland, Frederick Delius, Alphons Diepenbrock, Edward Elgar, George Enescu, John Field, Gerald Finzi, Cesar Franck, Luis de Freitas Branco, Robert Fuchs, George Gershwin, Philip Glass, Alexander Glazunov, Reinhold Gliere, Henryk Gorecki, Alexander Gretchaninov, Howard Hanson, Hamilton Harty, Paul Hindemith, Vagn Holmboe, Gustav Holst, Alan Hovhaness, Hans Huber, Johann Hummel, John Ireland, Giya Kancheli, Mieczyslaw Karlowicz, Charles Koechlin, Erich Korngold, Leopold Kozeluch, Jon Leifs, Douglas Lilburn, Franz Liszt, Sergei Lyupanov, James MacMillan, Bohuslav Martinu, Peter Maxwell Davies, Olivier Messiaen, Nikolai Myaskovsky, Goesta Nystroem, Arvo Part, Hans Pfitzner, Astor Piazzolla, Sergei Rachmaninoff, Max Reger, Steve Reich, Ferdinand Ries, Nikolai Rimsky-Korsakov, Christopher Rouse, Franz Schmidt, Alfred Schnittke, Robert Schumann, Peter Sculthorpe, Valentin Silvestrov, Bedrich Smetana, Louis Spohr, Charles Villiers Stanford, Igor Stravinsky, Karol Szymanowski, Eduard Tubin, Tomas Luis de Victoria, Heitor Villa-Lobos, Antonio Vivaldi, Carl Maria von Weber, Charles-Marie Widor, Alexander von Zemlinsky
For the last tier, there were dozens of close calls, where other composers might have gotten in as well.
This list of 121 composers leaves several big names unmentioned - on purpose. A few examples:
The renaissance and baroque periods are not represented well (Victoria, Vivaldi, JS Bach), because in general I am less attracted to this music. Several big names of this period did not come even close to making the 121 cut, including Monteverdi, Palestrina, Purcell, Corelli, Telemann, and perhaps most surprisingly Handel, whose works simply do not appeal to me.
The classical and romantic period are very well represented and there are very few big names missing. The romantic opera composers are the most noted exception, in particular Bellini, Donizetti, Rossini and even Verdi. Since I am currently finding a renewed interest in opera, that may change in the coming years. Outside opera, Wolf is perhaps the most surprising omission, since in general I love the Lieder genre that he is noted for.
The 20th (and 21st) century composers are reasonably well represented, including more than a handful who are still alive. Left out on purpose are big names like Bartok, Schoenberg, Webern, Xenakis and Stockhausen.
Of course, this list is not to be taken too seriously, since it is just my preference (be it one based on 25+ years of listening to classical music with a CD collection of several thousands). Still, if you like many of the composers listed here, you might want to sample the ones you do not know so well - chances are you will find something to like there!