I may be just a lurker on this forum (with a low post count and very basic knowledge of music in general), but I believe I have a bit of insight to share:
Nobody can be the greatest composer. The word 'great' is itself very subjective. This thread has so far only been about what your favorite composers are, and as far as I can see, it will never be about anything more.
I do notice Bach is on many of your lists. I myself am a big fan as well.
To make this post somewhat useful to any of you, my favorite composers are:
Me!
Bach
Chopin
Mozart
Uematsu
In that order, from most favorite to less favorite. (They're all 'favorites') Any composers not on that list fully deserves to be (these are just the first 5 that popped in my mind), as it is my belief that all music is worth hearing. Yes, even the heavy metal and videogame music and troubled teens with their guitar plunking.
And might I remind you all: Nature far predates humans. The birds and insects and whatnot; they were all making music far before we walked the earth. Respect them. I hope I've made a good impression of myself here. First posts on new forums are always exciting and a bit scary.
On a sidenote:
JohnGalt, who ARE you?
Does anyone know? 'Who is John Galt?'