Mary J. Blige
Blige is not a fan of using any bathroom that would be considered "public." In fact, every set she arrives in (and hotel room she stays in) must have a private bathroom, with a brand new toilet seat, just for her. Additionally, she refuses to stay in any hotel room that has a bed smaller than "king-sized."
George Clooney
Clooney has been known to make some outlandish requests for his dressing rooms. They're typically related to the roles he plays, but sometimes they go over the top. For instance, he requested a hot tub and a custom made beach hut while shooting "The Descendants." He also asked for a basketball court to be built for him while he was shooting the movie "Gravity."