Communications majors study verbal and nonverbal ways of communicating. They also study the impact of communications on a receiver. If you study communications, then you'll learn persuasion and how to build an argument. These teachings are especially helpful in copywriting because at its core, copywriting is simply putting together a persuasive argument. The copywriter wants a certain reaction from the reader, usually to buy something or to look upon it favorably.
Journalism majors write, edit and proofread a lot. They must also gain a wide range of knowledge of history and current events. They must be personable since they often conduct interviews, and people don't open up in an interview to someone without social skills. Their extensive background in writing, broad knowledge base and ability to work well with others are all skills that transfer well to a copywriting career.
English majors also write a lot, but they mainly write critical essays about literature. These essays are also arguments meant to persuade the reader to believe what the writer believes. When English majors aren't writing, these students are usually in class, continuing the persuasive discussions with classmates. This extensive background in written and oral persuasion is why an English degree is so useful to aspiring copywriters.
Advertising majors spend most of their time studying, critiquing and creating advertisements. Advertising majors cover every nuance of adverting, including copywriting. They also study the psychology behind why certain advertisements work and why some fail. Knowing the psychology behind advertising is an invaluable tool to copywriters because they create advertisements based on what they know people react to.
Marketing -- or as The Princeton Review puts it, "the art and science of getting people to buy stuff" -- is closely related to advertising. The main focus of marketing is to essentially get people to a product, which is what copywriters do, thus making marketing a solid choice for someone interested in becoming a copywriter.