From a previous answer of mine:
- Shut down the services you don't need
If you don't need a specific service, shut it down. One thing less to worry about, especially regarding security.
- Follow the least privilege principle
If a service does not need to have super privileges, just give it the privileges it needs. For instance, if your web application doesn't need to drop tables, there's no need to enable the drop privilege in MySQL.
- Have your services updated regarding security updates
This is very important! From time to time, security holes are discovered. It's very important to have your applications updated when it comes to security issues.
- Don't use default credentials
Just don't use it. They're evil :) For instance, MySQL's root user doesn't have a password. Create one.
- Backup everything that's important
Backup everything you need to rebuild your server, and I mean everything. Also, test your backups on a regular basis. This is valid not only for security reasons, but also for business continuity reasons. One never knows when a backup might be needed.
Hope this helps!