Old skool jazz tenors I have a soft spot for the very underrated Don Byas, for modern tenor players probably John Klemmer and Ernie Watts; for alto players as I am primary an alto player that is opening up a big can of worms - good call on Phil Woods check out his stuff with Quincy Jones, also Paul Desmond, Johnny Hodges, Dave Sanborn, Sonny Criss, Hank Crawford...
I'll pick James Carter as my favorite modern tenor player, who's a big admirer of Don Byas. Carter does a lot of crazy stuff, but he's a master of soulful ballads.
My old-school favorites are probably John Coltrane on tenor and Sonny Stitt on alto.
It's really hard to pick just one, though. (e.g. Scott Hamilton, Stanley Turrentine come to mind from those that haven't been listed yet)