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. But you can reset the password by editing the password field in the database.

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.

Select MD5 and change the password.

Don't know what phpmyadmin or mysql is ?
Don't worry. We offer this service for as low as $20.

If your website is hosted with us at Compitent Hosting then submit a Support Ticket or if you are not a Compitent Hosting customer yet,  use the contact us form to get in touch with us.We will recover your password. 

*This is a chargeable service.