If you just installed Linux or, separately, MySQL server, you need to undertake some simple routines to make it a little more secure. The below will set a password for a superuser account, remove anonymous user account and do some more sweet things.
sudo /sbin/service mysqld start /usr/bin/mysqladmin -u root password 'NEW_PASSWORD' /usr/bin/mysqladmin -u root -p -h localhost.localdomain password 'NEW_PASSWORD'
Anonymous account removal:
/usr/bin/mysql_secure_installation
Answers:
Change the root password? [Y/n] n
Remove anonymous users? [Y/n] y
Disallow root login remotely? [Y/n] y
Remove test database and access to it? [Y/n] y
Reload privilege tables now? [Y/n] y
