If you use encryption for securely storing passwords, you'll need to store the encryption "key" somewhere, too. This will be the "weak link", since if someone gets hold of the encryption key, they will be able to decrypt the encrypted passwords.
Since this is passwords that we're talking about here, a much better solution is to use a one-way hash. You hash the password when the user first creates it (preferably hashing with a salt value) and store the resulting hash value. Since hashes are one-way, no one can reverse the hash to the original plain text value.
To check that a users password is correct, you simply ask the user for the plain-text password, hash their input again and compare the resulting hash value with the hash value you have stored (taking salts into account of course). If the two hash values are the same, the user has entered the correct password.
Please see the following links for further info:
Hashing Password with Salt
For encryption (if you need to use that), I'd use Rijndael (AES).