Staying entirely in the '80s, early rap-rock would be the Clash, Time Zone and Tom Tom Club. Mid period would be RUN-DMC/Aerosmith and the Beastie Boys. Later would be Age of Chance, Pop Will Eat Itself, and World Domination Enterprises. You could probably give Big Audio Dynamite an honorable mention.
Anthrax?
Mr. Bungle, Red Hot Chilli Peppers, Faith No More.