According to about.com, money that is damaged and still clearly readable may be exchanged at any bank. Bills that are severely damaged are considered mutilated and must be mailed or hand delivered to the Bureau of Engraving and Printing.
Money that is not considered mutilated and is exchangeable at any bank includes bills that are dirty, torn, worn out, or defaced, according to about.com. Mutilated bills include those that have been damaged by insects, flood or fire. These bills should be insured and sent by registered mail with a return receipt to ensure safe delivery or compensation in the case of loss or damage.