For most types of projects you hire an independent contractor (IC) to do, the law does not require you to put anything in writing. You can meet with the IC, agree on the terms of your arrangement, and have an oral contract or agreement that is legally binding. Just because you can doesn't mean you should, however.
Oral agreements invite costly misunderstandings because there's no clear written statement of what the IC has agreed to do, how much you have agreed to pay, or what the two of you will do if a dispute arises.
These misunderstandings might be innocent -- you and the IC may genuinely remember your agreement differently -- or they may be intentional. Either way, it will be your word against the IC's, and there is no telling whom a judge or jury will believe. It's much safer to rely on a written document that clearly sets out the details of your relationship.
Even more important, a written independent contractor agreement helps establish a worker's independent contractor status by showing the IRS and other agencies that both you and the worker intended to create a hiring firm/independent contractor relationship, not an employer/employee relationship. (But don't expect the written agreement to be a magic bullet: A written agreement is useless if you treat the IC like an employee; for tips on structuring your work relationship with an IC in a way that will withstand government scrutiny, see Nolo's article Working With Independent Contractors: Avoiding Classification Problems.
A written independent contractor agreement should contain at least the following terms:
Other terms you could include range from copyright ownership to naming who will be responsible for the IC's employees.
Fortunately, an independent contractor agreement is something that you can create yourself. Two excellent sources for such agreements are Working With Independent Contractors (Nolo) and Consultant & Independent Contractor Agreements (Nolo), both by Stephen Fishman.