Many databases store sensitive information not about the system itself, but about end users. Social security numbers, credit card numbers and etc. are all sensitive data. On systems that store such sensitive data, it is important that the database dump be inaccessible to prying eyes. The easiest way to ensure this is to create the database dump in a folder that is marked 700 so that other users cannot list or traverse the folder.
If the dump file is to be transported off site, it should always be encrypted. Note that only the public key is needed for encryption purposes. This means that the system performing the encryption should never store the private key, at least not permanently. If the encrypted database dump is to be stored on tape, never include the private key on the same tape!