Jan is absolutely correct. This is, in fact, why for many people just doing a sole proprietorship is equally good to setting up an S corp. The S corp is harder to set up, often costs more, and can create more complex tax issues. Starting a corp is only useful for alleviating debt risk if your debtors allow you to sign for debts using the company name. In my experience, that is rarely true for a startup small business - mostly, you will have to sign your own name, which means you're still liable if the company goes belly up.
Here's my short list of reasons:
1) Required by law. Many states or municipalities require you to register your business, and can levy fines against you if you do not.
2) Legal protection for your trade name use. Some states (like Vermont, where I live) protect your right to use your own name for a business, like "Joe's Diner" or "Larrabee's Auto Shop" or "MacDonald Publishing". Other states don't, and if another company has already registered a name similar to "YourName Press", you can get sued for using it.
3) It's the professional thing to do. Take your work, your profession, your career seriously. Setting up a registered business is a part of taking your work seriously. If it also encourages you, like James mentioned, to take a look at all aspects of your business with a professional eye, so much the better.