After a recent, year-long re-discovery of his entire discography I can only say Stan Getz. If all someone knows about him is "Girl From Ipanema" then they know, well, hardly anything. His very best era was his last 10 years and he made it to his early 60s.
Some other names very worthy of being on the list:
Michael Brecker (!)
And then there's Napolean Murphy Brock, often known to command my complete attention...
It's gotta be the Saxophone Colossus, Sonny Rollins, but I'm conflicted about it. On any given day, every single one of the saxists listed might command top honors—Coltrane for breadth and intensity, Hawkins for consistency, Shorter for ingenuity, Getz because his sound is so sublime and accessible (like his greatest influence Lester Young's was). And then there's the folks not mentioned:
Dexter Gordon Lucky Thompson John Gilmore Gene Ammons David Murray George Adams Clifford Jordan
Another great tenor, Johnny Griffin, once said that as he got older, he'd be soloing and suddenly remember something—an augmented chord, harmonic resolution or whatever—that he'd completely forgotten about, though he'd obviously internalized it somewhere in the deep reservoir of a 50-plus year professional career. "I'm sure that happens to all of us," Griffin said, then added a joke. "And poor Sonny Rollins; he's probably forgotten more music than the rest of us ever knew." For anyone who cares, that's Rollins blowing on the Rolling Stones song, "Waiting On A Friend."
I voted for 'Trane, but I'm not sure that it's really all that meaningful. I don't -really- have a favorite, but he may just be dearest to my heart.
I saw a couple of DVDs last week -- the Cedar Walton quintet live (with George Coleman) and the Miles Davis quintet (with Wayne Shorter). Both were staggering. It was nice to be reminded of these folks who I haven't listened to much lately. With Shorter especially, I've been learning some of his tunes and falling into the trap of thinking of him mostly as a composer. The fact that he's had some weak periods contributes somewhat to that perception.
One of my very favorites that I haven't seen mentioned at all is Warne Marsh, who was a pupil of Lennie Tristano alongside of Lee Konitz. The CD 'Intuition' under Tristano's name is a must-hear. I also think that Warne's duet recordings with Red Mitchell are amazing.
I've probably heard more saxophonists live than have them on CD. The ones that have impressed me the most are Charles Lloyd and Jan Garbarek. Both have very distinctive, expressive nuances. Garbarek in addition have the company of an absolutely phenomenal percussionist, Marylin Mazur.
Tough choice between Coltrane,Shorter,and Henderson, but I have to say Coltrane, not only was he a great player,but the amount of innovation in such a short time is mind boggling! Most players took decades to achieve what he did in under 12 years. Amazing what he would have done had he lived longer.