World's Greatest Tenors

Bill Pierce is always overlooked.

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.

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.