Most of them. Since "game design" is not "game development", you don't need the hard science background that a computer science major ought to have, but you shouldn't ignore math and science altogether. Your design has to be feasible if you are ever going to get it implemented.
English: Most games have a narrative. Grammar and writing style help you present that accurately; and study of literature gives you styles and situations that you can adapt for your game's back-story.
History: Much like literature, this is a source of ideas and references. In an RPG, for example, you'll usually be creating a world with some history. Knowing what real people have done in real situations can make your world more believable.
Art: Obviously. The images are a large part of the character of a game. "Game artist" is a separate specialty, but closely related to design.
Music: Another important part of any game.
PE: This isn't like construction, where you're getting a workout on the job. You're going to be working at a desk for most of your career, and will have to develop exercise habits outside of work.
Math/Science/Technology: These are also obvious, so obvious that I almost left them out, but less important to design than to development. You do need to have an idea of what can actually be implemented.