It is common courtesy to give one's employer at least two weeks' notice before resigning. This gives the employer a sufficient amount of time to hire a replacement and handle any staffing issues caused by the resignation.
In most states, hourly at-will employees are not required to give any sort of notice when they want to resign. If an employee is salaried and has a contract, it may be required that he gives notice of his resignation within a specified amount of time before his last official day. If he has a contract and does not give the proper notice, he may face financial penalties, legal actions or other ramifications.