All TIME GREAT has to mean those who were most influential, changed the stylistic course of saxophone playing, and were most emulated. Using those criteria the first four on my list are no-brainers, the last will be controversia. In chronological order:
Sidney Bechet (played soprano, but has to be on the list)
Lester Young
Charlie Parker
John Coltrane
Dave Sanborn
Before you jump all over me for my fifth choice, like it or not, Sanborn was almost singlehandedly responsible for the
prevalence of the saxophone in pop music beginning in the early '70's. While clearly not a giant as far as harmonic sophistication in his improvisations, his style, way with a tune, and just plain "feel" in the context of most pop genres are unmatched. He spawned a slew of "Sanborn clones" and probably was responsible, as much as anyone, for the "smooth jazz" movement. Why is that important? Because at a time when jazz was in danger of becoming even more of an obscure art form than it already was, "smooth jazz", as much as we like to put it down, opened the door for many listeners who went on to understand and appreciate real jazz.
Lots of great choices in the previous posts, but most of them have roots that can be directly traced to Bechet, Young, Bird or Coltrane. Other greats, not mentioned, that are personal favorites:
Gene Quill
Charlie Mariano
Bob Mover
Jimmy Heath
Tina Brooks
Ike Quebec
Serge Chaloff
Pete Christlieb
Dave Liebman
Steve Grossman
Bob Berg
Kenny Garrett
Frank Wess
Frank Foster
Zoot Sims
Harold Land
James Moody
Sal Nestico
Benny Golson
Earl Bostic
Sonny Criss
Jackie McClean
Bud Shank
David Newman
