You should not ever need to remember the user's password - to do so is a violation of their trust and presents a security hole.
Normally you will hash the password with MD5 (these days it's better to use SHA-2), and when the user submits their password to try and log in, hash that password as well, and see if the hashes are a match.
For added security, you can create a "salt" column to the database and generate a random salt when the password is first submitted. Add the salt to the beginning of the password, and then hash it. Store the hash of the salt+password, and the salt together. Now when the user submits his password to log in, you would combine it with the salt, hash it, and check if the hash is a match.
The salt ensures that if multiple users have the same password (chances are they do), their password hashes will not be identical.
If the user forgets their password they will have to provide a new one, simply storing their password and sending it back to them when they forget is bad practice and a sign to the user that you aren't handling their privacy very well.