The answer depends on the state in which you live. Many states allow either party to appeal within a certain period of time, usually between 10 and 30 days, and obtain a new trial. In many states, appeals must be based solely on the contention that the judge made a legal mistake, and not on the facts of the case. Other states have their own unique rules. For more information, see Nolo's article Appealing a Small Claims Court Case.