World's Greatest Tenors

There are the absolute legendary forefront artists, to be sure.
Music is both science and magic. The first has to be learned to a point where it can then be put away and forgotten, then the art begins.
All new and fresh things. Music is the truest art form.

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.

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,