Everywhere I have seen people talking about storing passwords in a database, they have almost always used MD5.
What is wrong with AES, or SHA1?
Because AES encryption is symmetric. Given a password encrypted with AES and the key, you can decrypt the password. This is undesirable, because you almost always want only the owner of the password to know it and don't want to have an easy way to derive the password. The SHA and MD5 algorithms, on the other hand, perform a (mostly) one-way transformation of the password. There is no piece of information (key) that allows you to return the transformed password back to its plaintext form.