1. John Coltrane
I think this pick is a no brainer. Before Coltrane churned out classic after classic as a bandleader, he played on tons of classics in the 40s and 50s. He was the best bebop saxophonist, but decided to push the boundaries and became one of the founders of avant-garde jazz. He was the best then, and he still is.
Notable albums: A Love Supreme, Giant Steps
2. Albert Ayler
Albert Ayler once said, "Trane was the father, Pharoah is the son, and I'm the holy ghost." Or something like that. I'm not positive about the wording. Anyways, the quote makes sense. He took all the innovations that Trane and Pharoah had made, and pushed the saxophone even further into the avant-garde with astonishing results.
Notable albums: Spiritual Unity, Spirits Rejoice
3. Ornette Coleman
Coltrane may have been one of the founders of free jazz, but no one had as much of an impact as Ornette Coleman. He was playing outside of time signatures and chords in the mid-50s, when bebop was still considered progressive and wild. And Coleman has shown consistency, as he has consistently innovated for the last 55ish years.
Notable albums: The Shape of Jazz To Come, Science Fiction
4. Anthony Braxton
Anthony Braxton is often overlooked, but his prowess on saxophone (and many other reed instruments) is comparable to pretty much any body. He has dealt exclusively in the realm of avant-garde jazz and has composed some of the most interesting and complex saxophone pieces ever. And, like Ornette Coleman, he has been putting out great material for decades.
Notable albums: For Alto, 3 Compositions of New Jazz
5. Charlie Parker
I'm not as well versed in Charlie Parker's playing, but what I've heard is pretty remarkable. His sound is furious and chaotic, and he did what he did at a time when Louis Armstrong was still the king of jazz. Though he certainly stayed within the parameters of bebop, his wild playing and disregard for the rules definitely influenced free jazz.
Notable albums: Jazz At Massey Hall (with The Quintet), Charlie Parker
6. Pharoah Sanders
I know Pharoah Sanders best for "The Creator Has A Master Plan" off of his masterpiece, Karma. This 33 minute odyssey finds Pharoah and his good sized band (complete with yodeling) making continual psychedelic free jazz noise, which also happens to be quite beautiful sometimes. He was crazy, innovative, and had an extreme lung capacity.
Notable albums: Karma, Deaf Dumb Blind
7. John Zorn
The first (and only, I think) Jew on the list, John Zorn is also one of the most prolific sax players. For the last twenty to thirty years, he has been composing massive amounts of jazz and experimental music, nearly all of it good. But he's not just a great composer. He's a master saxophone player as well. His unkempt squeal is immediately recognizable and awesome.
Notable albums: Naked City, Alef (with Masada)
8. Peter Brotzmann
I clearly have a preference for free jazz, but that's because it's more fun. And Peter Brotzmann is all kinds of fun. Sort of. His sax playing is easily the most intense and dissonant and chaotic of anyone's on this list. His pieces (especially Machine Gun) are far heavier than any metal album, but they're also thoroughly interesting.
Notable albums: Machine Gun, Little Birds Have Fast Hearts
9. Rahsaan Roland Kirk
What impressed me initially (well, and still does impress me) was the fact that Rahsaan Roland Kirk often plays more than one instrument at a time with excellent ability. That alone would get him on this list. When you factor in that the music he creates is smooth while still being chaotic, that bumps him into the top ten. Not to mention: he's blind.
Notable albums: The Inflated Tear, Bright Moments
10. Roscoe Mitchell
I might be a little biased based on Mitchell's Chicago ties, but his playing is truly great. his style is unique, he has unbelievable technical ability, and he has been a free jazz innovator for over forty years. As the leader of the Art Ensemble of Chicago, he has composed and performed some of the best jazz of the last several decades.
Notable albums: Sound, Live In Paris (with the Art Ensemble of Chicago)
And roundin' out the top 20...
11. Eric Dolphy
12. Archie Shepp
13. Sonny Rollins
14. Cannonball Adderley
15. Wayne Shorter
16. Dexter Gordon
17. Ken Vandermark
18. Stan Getz
19. Maceo Parker
20. James Chance
(The last two may not be jazz, but they're worthy sax players)
That's what I think. Granted, I've never touched a saxophone in my life. But my friend plays.