World's Greatest Tenors

I would like to add the following

Jazz - my personal favorite is Dexter Gordon
Opera - not sure if he qualifies "yet" for world's greatest but he is on the top the list of current tenors, Juan Diego Florez. Specially when comes to Rossini operas.

Btw, Tia's band is all female. (beside the trumpeter) Yeah, the drummer also, really :)

Charles, agree on Dexter, and "Prez" would have been on my list if it had been four instead of three. I listed three only because the OP listed three. Since he didn't say "favorite" but "greatest", "greatest" seems to imply "most influential" since anything else is subjective. I think who the most influential have been is pretty well established and agreed upon by knowledgable fans and critics. I also like Acman3's choice of Wayne Shorter, besides being a great player was one of the very best jazz composers. So, for stature and influence:

Hawkins, Prez, Trane, Sonny, and I am tempted to add Joe Henderson

For listening pleasure:

The above and I would add Dexter, Getz, Zoot Sims, Charles Lloyd, Johnny Griffin, Hank Mobley

And for sheer virtuosity (ability to do anything on the instrument from a technical standpoint), IMO the greatest ever virtuoso on the instrument has to be Michael Brecker.

Hi Frogman,
Good points,
Virtuoso? wow, really tough to say. Certainly Coltrane and I'd have to put James Carter on this plane as well. Joe Henderson is an under appreciated but massive talent! You could make a very favorable comparison of his work vs Wayne Shorter(the better known). The more I think about it Sonny Stitt was a virtuoso if there ever was one, total mastery of the saxophone in any genre he chose. I could discuss this topic for days as I have such admiration for these extraordinary musicians.
Charles,

Frogman,
You always present a very reasoned perspective and commentary which I sincerely appreciate. On pure technical prowess I get your point about Brecker's status. The thing is though I approach music as such an art form that I judge the musicians on the overall package they have to offer and my emotional reaction to how they play. So the ones who pull me into their music the deepest (and keep me there as well) are more compelling and influential in my estimation.

On technique I've read the same about Jimmy Dorsey on alto sax (flawless they said) yet I'll take Charlie Parker in an instance for actually listening to and enjoying (no slouch when it comes to technique eithe). I'm most moved by the musician's ability to communicate and connect with emotion.
Charles,