You cannot recover the existing password, but you can reset it to a new password.
The passwords are stored using a one-way MD5 hash which prevents recovering the password. However, you can reset the password by editing the password field in the database. We set the password to a known value and then you may log-in using that new password.
The password is stored in the MySQL database jos_users table password field. (change this for your table prefix if different)
Use a MySQL utility such as phpMyAdmin or MySQL Query Browser to edit this field.
Open the table, find your admin username, and then select that row for editing.
The password must be hashed, you cannot simply enter text into this field.
Set the password to a known value:
Paste the hashed password into the field, save the change, and log-in using the new password.
Immediately change your password to something more secure!