One note is to secure MySQL, I don't know for sure but I believe you could login to MySQL remotely with no password during this operation (I'm not sure, maybe it doesn't accept blank passwords but I firewall MySQL port anyway and recommend you do the same).

First edit /etc/my.cf

Under the [mysqld] field add the following line somewhere:

skip-grant-tables

Now restart mysql: service mysql restart or on Debian style systems: /etc/init.d/mysqld restart

You can now login to mysql as root with no password.

mysql -u root

Enter the following commands (you can copy and paste below, remember to change "YOURNEWPASSWORD" to whatever you want the password to be.

use mysql;
UPDATE user SET password=password("YOURNEWPASSWORD") WHERE user='root';
flush privileges;
quit

*Note more note is that if you are using Plesk, the root user is probably called/renamed "admin" so you'll need to replace everything above with "admin" if that's the case.  Of course an easier way if Plesk is actually running is to use the Forgot Password function of the Control Panel itself.