Well, experts in the subject affirm that 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.
If for some reason you would to reset your Joomla! admin password, or if you need to offer admin access to somebody else, please change it by doing the following:

For more info and explanations, check this post over here: http://forum.joomla.org/viewtopic.php?t=10985).