I had been looking for a solution to this issue for a while now and today it hit me like a truck! What I needed was a way for SharePoint to email out when the Health Analyzer detected any problems with the Farm. A TechNet article vaguely says you can configure this, but gave no further information on how. After searching and reading, it finally hit me. The Health Analyzer sends all alerts to a Health Reports list in Central Administration. Being a SharePoint list, you can simply subscribe to alerts here and get notified of when new issues arise. Doh!
Here is what you want to do:
1. Open Central Administration, and click on "Review problems and solutions".
2. This will take you to the Health Reports list. Simply click the "List" tab to get the Ribbon options.
3. Click on "Alert Me" and set your options accordingly.
Pretty simple. There are some other options like custom code, but this is a very straight forward and easy implementation for end users to take advantage of.