Where to begin!?...
Obviously, as others have stated, The Rock, from late 1997 - Mid 2001 was hands down, the best Promo man in the business. His ability to not only be hilarious, but also serious when he needed to be made him gold on the stick.
Chris Jericho during his late 1997 - 1998 temper tantrum days in Dubya-C-Dubya was excellent! His "Gene Mean", "Man of 1004 holds", "Quasi Juice" and "Greenberg" promos were awesome! Which led him to being the best home-grown heel WCW had at the time. His work in the WWF from 1999 - 2001 was excellent too!
Kurt Angle from 2000 onwards was dynamite on the stick too! I fondly remember his mic work during his 2002 feud with Rey Mysterio in the build up to Summerslam. Some of his best work was during that time.
Scott Hall was pretty good too, throughout his career, as Razor Ramon he played up that character well during promos and obviously, was a major reason why the nWo reached the heights in popularity that they did in WCW from '96 - '98.
Paul "Giant/Big Show" Wight has always been able to cut believable promos. It's a shame that he doesn't have the same aptitude for in-ring ability that he does for being able to talk. Go back and watch some Big Show/DX/Rock goings on from 2000 and tell me the man cannot talk! It's a shame that he quit working out at some point in 1997 and let himself go. He had the potential to be something really special in Wrestling.