Probably the most well-known association of artists using a Shure microphone is Roger Daltry from The Who. He has his Shure SM58 microphone taped up on the XLR connector as he likes to swing the mic by the cable during the performance.
Other notable artists that use Shure microphones are the likes of Marcu Mumford from Mumford and Sons who was one of the very first users of the Shure KSM8 microphone before it was released to the public.