Jack White
Jack White became notorious for requesting a ton of guacamole along his tour. However, he was so particular with the chunkiness of the guacamole that he sent each venue a recipe with clear instructions on how to make it. He also hates bananas, and he adds "PLEASE NOTE: this is a NO BANANA TOUR" on all of his riders.
Eminem
Eminem never cared about furniture or any other strange request that other celebrities put forward regularly. He only cares about what food is available in his dressing room. The weirdest requests he's had were for six Lunchables (three turkey and cheese, three ham and cheese), 24 cans of Diet Coke, and 24 additional bottles of Diet Coke. This is all just for him, by the way.