Here are some of my favorite composers and favorite pieces by them - I will list only the top fifty, though I could list hundreds...
1. Beethoven (for his amazing string quartets and symphonies, but not his overtures)
2. J.S. Bach (particularly for the cello suites, the six sonatas and partitas for unaccompanied violin, and the Goldberg Variations)
3. Bartók (for all his chamber music, but especially the six quartets, also his viola concerto, and his Music for Strings, Percussion, and Celesta; Concerto for Orchestra; Divertimento for String Orchestra; Violin Sonata No. 2; Piano Concerto No. 3)
4. Haydn (for being the father of the string quartet and inventiveness in writing 68 string quartets)
5. Mozart (particularly his late string quartets and quintets, and of course the Sinfonia Concertante, and Duos for Violin and Viola; Requiem; late symphonies)
6. Dvořák (great later string quartets and chamber music; Serenade for Strings, Op. 22; Rusalka; Symphonies 6-9; Husitska Overture; Cello Concerto)
7. Sibelius (for his amazing symphonies and tone poems; and everything; particularly Symphony No. 7; Tapiola; Finlandia; Symphony No. 4; Valse Triste; Lemminkainen Suite; String Quartet "Voces Intimae"; Symphony No. 5; and my favorite Violin Concerto of all time...)
8. Shostakovich (primarily for his 15 symphonies and 15 string quartets)
9. Scriabin (particularly for his ten piano sonatas, all amazing; also his Piano Concerto in F sharp minor, Op. 20; Prometheus: The Poem of Fire, Op. 60)
10. Hindemith (for his concerti for all instruments of the orchestra, particularly his four viola concerti: Der Schwanendreher, Kammermusik No. 5, Konzertmusik, and Trauermusik, also his symphonic writing: Symphonia Serena; Symphonic Metamorphosis of Themes by Carl Maria von Weber; Mathis der Maler; not to be forgotten string quartets and his final Oktett; the four unaccompanied viola sonatas, especially Op. 25/1)
11. Debussy (for the string quartet; Prelude to the Afternoon of a Faun; La Mer; and the Sonata for flute, viola and harp)
12. Ravel (for Daphnis and Chloe Suite No. 2; String Quartet; Bolero; La Valse; and the orchestration of Mussorgsky's Pictures at an Exhibition)
13. Berg (for the amazing opera: Wozzeck; Violin Concerto; and his amazing String Quartet, Op. 3; Lyric Suite)
14. Schoenberg (for his Suite/Septett for Three Clarinets, Piano, and String Trio, Op. 25; his String Trio, op. 45; his Violin Concerto; his Verklärte Nacht (Transfigured Night), Op. 4, for string sextet (1899); Pierrot Lunaire; and the Fantasy for Piano and Violin, Op. 47)
15. Brahms (for his Symphonies, chamber music, Tragic Overture, and Piano Concerto No. 2, my favorite piano concerto)
16. Schumann (for the wonderful Symphony No. 1 "Spring"; Piano Quartet; Piano Quintet; and great Cello Concerto)
17. Schubert (for his lieder; "Death and the Maiden" Quartet; String Quintet with two celli; "Arpeggione" Sonata)
18. Glazunov (for the best Russian string quartets, aside from Shostakovich and Prokofiev, particularly String Quartet No. 2, 3, 5, and 7)
19. Smetana (for his String Quartets No. 1 "From my Life" and No. 2; for his wonderful Piano Trio in G minor; Ma Vlast; and The Bartered Bride)
20. Puccini (for Madama Butterfly; Tosca; La Boheme; Girl of the Golden West; Il Trittico)
21. Richard Strauss (for the many tone poems, particularly Also Sprach Zarathustra, An Alpine Symphony; Don Quixote; and Don Juan; operas: Der Rosenkavalier; Elektra; Salome; Four Last Songs; Metamorphosen for 23 solo strings; Le bourgeois gentilhomme orchestral suite)
22. Mahler (for his 10 symphonies; Kindertotenlieder)
23. Verdi (for operas: La Forza del Destino, Rigoletto, il Trovatore, Otello, Nabucco, I Vespri Siciliani, Un Ballo in Maschera)
24. Vivaldi (Violin Concerti such as The Four Seasons; chamber music)
25. Stravinsky (for The Rite of Spring; The Firebird; Petrushka; Pulcinella; L'Histoire du soldat; Violin Concerto; Concertino for String Quartet; Three Pieces for String Quartet; Feu d'artifice)
26. Handel (for the Messiah; for the Trio Sonatas with Flute, Violin, Cello, and Harpsichord, Op. 2)
27. Tchaikovsky (for his "Pathetique" Symphony; Violin Concerto; Snegurochka; String Quartet No. 2 in F major, Op. 22; Symphony No. 5 in E minor)
28. Mendelssohn (for his Octet; 6 String Quartets; his "Italian" Symphony; Violin Concerto)
29. Prokofiev (for his 2 string quartets; his Sonata for Two Violins, op. 56; Lt. Kije Suite; Suite from the Love for Three Oranges; Peter and the Wolf; "Classical" Symphony; 5th Symphony)
30. Vaughan-Williams (above all for his marvelous Fantasia on a Theme of Thomas Tallis; also the String Quintet; Symphony No. 5; Flos Campi; Riders to the Sea (opera))
31. Bloch (for Schelomo (1916); Concerto Grosso No. 1; String Quartet No. 1; Baal Shem; Kol Nidrei; Suite for Viola; Suite "Hebraique"; Suite for Solo Viola (unfinished); Night for String Quartet)
32. Nielsen (for the four string quartets, particularly Op. 11 in F Minor; Masquerade)
33. Zemlinksy (for the four string quartets, particularly No. 1 and No. 4; Der Zwerg)
34. Humperdinck (for Der Konigskinder)
35. Satie (for Gymnopédies and 7 Gnossiennes; Je te veux; Le Fils des étoiles)
36. Falla (for The Three-Cornered Hat; El Amor Brujo)
37. Ginastera (for String Quartet No. 2, op. 26; Pampeana No. 2 for cello and piano, op. 21)
38. Villa-Lobos (for his String Quartets Nos. 5, 6, and 17; Bachianas Brasileiras Nos. 1, 5, and 7; Assobio a Jato; Duo for violin and viola (1946))
39. Berlioz (for his Harold in Italy; Symphony Fantastique; "Corsair" Overture; Roman Carnival Overture; Les nuits d'été)
40. Szymanowski (for the Mythes for violin and piano; String Quartet No. 2)
41. Saint-Saens (for Danse Macabre; Violin Concerto No. 3; Introduction et Rondo Capriccioso; Violin Sonata No. 1; Carnival of the Animals; "Organ" Symphony)
42. Franck (for the Violin Sonata; Piano Quintet; String Quartet in D Major)
43. Faure (for his Piano Quartets; String Quartet; Pavane; Requiem; Pelléas et Mélisande Suite)
44. Ligeti (for his Viola Sonata; String Quartet No. 2; Violin Concerto)
45. Elgar (for his String Quartet; Piano Quintet; Violin Concerto; Enigma Variations; Serenade for Strings; Sospiri; Introduction and Allegro for String Quartet and String Orchestra)
46. Menotti (for his operas, such as The Old Maid and the Thief; Amahl and the Night Visitors)
47. Barber (for String Quartet, Op. 11; Capricorn Concerto; Piano Concerto; Violin Concerto; Dover Beach; Knoxville: Summer of 1915; Essays for Orchestra)
48. Bernstein (West Side Story; Candide Overture; Trouble in Tahiti; Serenade, after Plato: Symposium, for solo violin, strings and percussion; Symphonic Suite from "On the Waterfront"; Mass)
49. Copland (for Appalachian Spring; Billy the Kid Suite; Rodeo Suite; Symphony No. 3; Piano Variations; Clarinet Concerto)
50. Rachmaninov (for Francesca da Rimini (opera); Piano Concerto No. 3; Symphony No. 2; Vocalise; Symphonic Dances; The Bells; Symphony No. 1; the piano music; the piano trios)
Now, obviously I would have loved to have listed many more outstanding composers like Wagner, Bruch, Grieg, Borodin, Tanayev, Khachaturian, Joachim, Rimsky-Korsakov, Mussorgsky, Resphigi, Kurt Weill, Ives, Piston, Carter, Hanson, Chopin, Glinka, Chausson, Schnittke, Britten, Holst, Walton, Coleridge-Taylor, Kodaly, Dohnanyi, Serly, Revueltas, Chávez, Bax, Bridge, Milhaud, Bruckner, Crumb, Messaien, Dukas, Schulhoff, Martin, Martinu, Bizet, Massenet, Ysaye, Poulenc, Arensky, Stockhausen, Xenakis, Antheil, Castelnuovo-Tedesco, de Bériot, Purcell, Rameau, Gesualdo, Monteverdi, Frescobaldi, Biber, Gluck, Stanford, Benjamin, Hummel, JC Bach, des Prez, Buxtehude, Albinoni, Corelli, A. Scarlatti, D. Scarlatti, Clementi, Tartini, Leclair, Arriaga, Boccherini, Vieuxtemps, Johann Strauss, Spohr, Berwald, Donizetti, Massenet, Delibes, Delius, Paganini, Rossini, Gliere, Granados, Gade, Raff, Hoffstetter, Hoffmeister, Dittersdorf, Janacek, Lalo, Kreisler, Turina, Hugo Wolf, Weber, Webern, Herrmann, Marais, Korngold, Liszt, Offenbach, Cage, Reich, Sarasate, Goldmark, Penderecki, Lutoslawski, Wieniawski, Bacewicz, Gubaidulina, Kalliwoda, Jolivet, Sculthorpe, Seitz, Alfvén, Beach, Stamitz, Quantz, Yun, Ung, Hahn, Ole Bull, Persichetti, Rodrigo, Rolla, Rautavaara, C.P.E. Bach, Schikele, Berio, Boulez, Dutilleux, Orff, Suk, Lyadov, Rochberg, Griffes, Tippett, Lou Harrison, Honneger, Boulanger, Jongen, Imbrie, Diamond, Harris, Onslow, Alan Rawsthorne, Chaminade, Viotti, Wranitzky, Tarrega, Ponce, Soler, York Bowen, Quincy Porter, Hall Overton, Feldman, Crawford, Rebecca Clarke, Maconchy, Dame Ethel Smyth, Zwilich, Pärt, Harry Partch, Henry Cowell, Saygun, Schuman, Sallinen, Salonen, Subotnick, Piazzola, Jerry Goldsmith, Rota, Morricone, Kagel, Varese, etc. but had to limit it to only the top 50. Sorry to you other amazing composers who didn't make the list... And please drop me a line and let me know if I left out someone by mistake who needs to be included in the TOP 50.
Ah! any romantic composer of the 19th century.... but Beethoven is unequalled in the history of music. It's hard to believe he was human!! Probably an extra-terrestrial or some special incarnation of the Muses of Music!!