Ooh, he's good.

I don't know about composer, but Paul McCandless is like, the best jazz oboist in history.

My favorite jazz composer is Miles Davis.
I also love Jerome Kern, Gerwshin Thelonious Monk and many others.

Well that's a tricky question, cos every jazz player sort of composes, in real time. But refering to written melodies and rhythm sections, erm, Charlie Parker comes to mind right now =)

Wynton Marsalis, George Gerswin, George Winston, Count Basie, Louie "Satchmo" Armstrong, Benny Goodman, Glenn Miller...