I'm sure this has been done here before, but I sometimes try to list the greatest, actually that list can change from day to day.
My list is very personal, and certain composers considered great are not in it. This is also a very 'traditional' kind of list, even if some of the names are virtual unknowns.

1. JS Bach
2. Beethoven
3. Mozart
4. Schubert
5. Schumann
6. Chopin
7. Palestrina
8. Faure
9. Prokofiev
10. Brahms
11. Dufay
12. Handel
13. Buxtehude
14. Byrd
15. R.Strauss
16. Mussorgsky
17. Schuetz
18. Dvorak
19. Vivaldi
20. Tchaikovsky
21. Bizet
22. Lassus
23. Elgar
24. St Colombe
25. D. Scarlatti
26. Scriabin
27. G. Gabrieli
28. M.-A. Charpentier
29. Purcell
30. Victoria
31. Telemann
32. Wagner
33. W. Lawes
34. Rameau
35. Weber
36. Tallis
37. R.White
38. Liszt
39. Debussy
40. Monteverdi
41. Mendelssohn
42. Ravel
43. Smetana
44. Rimsky-Korsakov
45. Frescobaldi
46. Zelenka
47. Szymanowski
48. Berlioz
49. Froberger
50. Enescu
51. F.J. Haydn
52. Josquin
53. Keiser
54. Poulenc
55. Mondonville
56. Corelli
57. Morales
58. C.P.E. Bach
59. Borodin
60. Rossini
61. Kalomiris
62. Janacek
63. Meale
64. Carissimi
65. Hassler
66. F.Couperin
67. Delius
68. G.Holst
69. Bruckner
70. F.M. Veracini
71. d'Indy
72. Puccini
73. Balakirev
74. Gorecki
75. Gluck
76. Bernstein
77. Saint-Saens
78. Lully
79. Verdi
80. Sibelius
81. Grieg
82. Rachmaninov
83. J.Strauss II
84. Marenzio
85. Hummel
86. D.Lobo
87. Bartok
88. Hummel
89. Khachaturian
90. Falla
91. O.Gibbons
92. Hindemith
93. Skalkottas
94. Gershwin
95. Clementi
96. Walton
97. Martinu
98. Tubin
99. Rubbra
100. Granados

Can't stop

101. Mundy
102. Cherubini
103. Delibes
104. Magnard
105. Weiss
106. Stravinsky
107. Bortniansky
108. Berg
109. W.F. Bach
110. Massenet

Mr Haydn at no.51. Care to share why? I am curious. Thanks.

I thnk this has been done before but I dont mind answering again - I am very impressed that you are able to list so many composers though I prefer to just list my favourite 5 (in no particular order):

Jean Sibelius
Ludwig Van Beethoven
Dmitri Shostakovich
Pyotyr Ilyich Tchaikovsky
Gustav Mahler

Other composers I like include Bach, Bruckner, Chopin, Debussy, Mozart, Ravel, Vaughan Williams etc, though not sure how I would rank them outside of the top 5 .

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“Music is a moral law. It gives soul to the universe, wings to the mind, flight to the imagination, and charm and gaiety to life and to everything.” ~ Plato

“The aim and final end of all music should be none other than the glory of God and the refreshment of the soul.” ~ Johann Sebastian Bach

My guess would be that there are fifty others that he likes more. I would rank Haydn in my top four, on some days even as high as number two. But any sort of ranking order is debatable. But it's fun as long as people don't take it too seriously.

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Martha doesn't signal when the orchestra comes in, she's just
pursing her lips.

Interesting to see an Australian on the list. Richard Meale died just last year, and not much attention was paid to a thread I created in tribute. He was a composer who wrote music in many styles from neo-classical to atonal and everything in between. How did you come across him, may I ask?...

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"Contrary to general belief an artist is never ahead of his time but most people are far behind theirs" - Edgard Varese

Wow, that's kind of funny that Bruckner is not included in that massive list of 100 composers. With guys like Falla and Lassus included...

Conor those are some good top picks!

No John Cage??? I read one of his composition is a mind-changing work.

It's definitely been done before.

Overdone if anything.

Greatest = populist?

Greatest = most played?

Greatest = most prolific?

Lists don't do anything for me I'm afraid. Anything in the top 46 should be instantly wiped out :P

Greatest = most original would an interesting concept to define - in which case, the modern music of the 20th century comes into the fore...

When it comes to music, or the domain of art, superlative comparisons don't have much intrinsic value. A composer's music is a relationship between a listener, and a composer for me: it makes more sense to view it as a relationship, rather than a financial asset with the greatest stock index, or perhaps the greatest FTSE/Wall Street gains.

Far from being pedantic, the 'Greatest Composers' mentality has probably spurred the neglect of many other exciting composers, and is a mindset spurred by a commercial agenda of its own. It's lovely that many can appreciate Bach and Beethoven. Maybe they could try doing it without proclaiming their own taste as 'the greatest' hmmm?

I have tried to 'get into' Haydn but failed...

Of course there are I think some objective reasons...his music on the whole is much lighter, less deep, than those of the other members of the 1st Viennese School..

His music is entertainment, rather than expressing all the states of the human condition

Of course I am speaking in generalities and others may vociferously dispute these contentions..

I have heard Haydn likened to the 'muzak of the 18th century'...I wouldn't go that far at all, as I do admire Haydn, (also his brother Michael was no mean composer)..for that matter I have admiration for all on that list. Notice I did call the list, 'Great Composers'...
I don't view Haydn as in the upper echelons though.

I am Australian

Unfortunately, Meale is neglected even in this country...
Percy Grainger and Arthur Benjamin also came very close to making that list.....

My feelings about Bruckner (and also Mahler) are too equivocal.
I certainly don't deride Bruckner, his music sometimes is overwhelming. But I added a caveat at the beginning as to who I would include.

I have less qualms about omitting Shostakovitch, but that just may be a personal thing.

Oh by the way, I edited the list

111. Nielsen
112. Gombert
113. Ginastera
114. Machaut
115. A. Merikanto
116. Boccherini
117. V.Novak
118. Sorabji
119. Berwald
120. Zemlinsky
121. A. Scarlatti
122. Karlowicz
123. Busoni
124. J. Sheppard
125. Grainger
126. Hanson
127. Reger
128. Liadov
129. Chausson
130. S.Barber=Miaskovsky=Glazunov=M.Haydn

I love how this thread has turned into some sort of personal blog. Very well, I will give 20 - and I refuse to give any more - it's hard, but I'll try it. Maybe the tiered method will help me not have a mental breakdown on having to decide on who goes in slots numbers 1-10.

1st Tier: Bach, Beethoven, Mozart, Prokofiev
2nd Tier: Bartok, Schubert, Schumann
3rd Tier: Bruckner, Mahler, Sibelius, Varese
4th Tier: Medtner, R.Strauss, Villa-Lobos
5th Tier: Liszt, Rameau, Stravinsky
6th Tier: Alkan, Pachelbel*, Ravel

Ouch - I feel extremely, extremely boring... not worthy of the honorable list you have provided. Maybe I should have thrown in Eiges or Pierne to bring myself up a notch - but no, I tried to be as honest as possible.

*

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“I thought with fury of the wonderful American orchestras that cared nothing for my music; of the critics who repeated for the hundredth time, 'Beethoven is a great composer,' while balking violently at new works; of the managers who arranged long tours for artists playing the same hackneyed programs fifty times over.” ~ Serge Prokofiev