Bruce Springsteen, Micheal Jackson, and Prince declined performing at Live Aid.
"Bruce Springsteen could not play at Live Aid, despite his huge popularity in 1985, because he was doing his Born In the USA Tour which was obviously sold out but he allowed his stage to be used in London. Michael Jackson and Prince also did not play (although Prince did send a pre-taped video of an acoustic version of 4 The Tears In Your Eyes, which was played during the concert.)"
Maybe the question was bit vague, but I was thinking of Prince, Springsteen and Jackson, who were at their commercial peak and probably the best-selling artists in the world at the time.