Unattended automatic security updates / upgrades
Please also keep in mind there are '0-day' vulnerabilities out there, which can be used to compromise your website even before Drupal publishes a security advisory and corresponding patch. And that even if you use an automated update for Drupal core, there still will be a time window in which your site was vulnerable.

The best way to deal with these kind of issues is therefore to have all your Drupal code in a version control system - Subversion or Git for example. This way you can easily:  
- identify when there has been an intrusion with a status command (this will show you all modified files in your source files)  
- reverting these changes, and therefore repair all harm done, by resetting the source tree to your latest commit

The only downside is that you have a little more work to do with each update, as you need to commit all changes back to your repository after each code change. But this is a very small price to pay for the added benefits and piece of mind this provides.