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?
The main reason why using symmetric (or asymmetric) encryption is not advisable for protecting passwords is: key management. When using encryption, you must protect the encryption key (or the entropies from which the key is derived). And protecting the key is a very difficult task to solve. Hashing (with SHA, MD5, or any other algorithm) solves the problem of key protection, because you don't need to keep any secret value (other than salt, but salt is significantly less sensitive than encryption key; you can store salt in plain text). So if you only keep passwords for authentication purposes (performed by your app), there is absolutely no reason to use encryption; hashing would do just fine. However, there may be cases when you need to be able to decrypt passwords (e.g. you may need to pass users credentials to third party apps). This is the only case, in which the use of encryption would be justified for password storage.