the test account and database that were created during the initial installation
Login to mysql as root, from the command prompt “shell> mysql –u root –p mysql” and enter the password when prompted
mysql> drop database test;
mysql> use mysql;
mysql> delete from user where user='test';
mysql> delete from user where user='';
mysql> flush privileges;
Make sure that each account has a password set
Do not grant global privileges unnecessarily
Avoid using wildcards in the hostname value associated with accounts
Periodically review users and databases that are setup in MySQL
Do not use passwords on the command line. From the command line you can login to MySQL using "shell> mysql –u root –password=somepassword mysql" the problem with this is anyone on the server could view your password with a simple process list command "shell> ps". The correct usage would be: "shell> mysql –u root –p mysql", from this MySQL will prompt your for your password and it will not show up in the process list as plain text.
Note: There are many excellent articles available on the web for MySQL security. Go to your search engine of choice and search “securing mysql” and you should have reading for weeks.