Great Tools for troubleshooting Google Apps: Mail, (MX & DNS records), Calendar and general errors or issues that you may encounter with Google Apps services. The message header analysis tool is excellent for making the server, hops, delays and general email message routing understandable and readable.
The MX Tool Box is also a great utility for all sorts of things like DNS look ups, SPF record checks, SOA IP addresses and to gauge the general conformity of a providers implementation against best practices!
If you’re ever trying to figure out where a website is hosted, Host Advice provides a tool that reveals the web hosting service behind any domain as well as nameservers and other useful information.
What tools do you find the most useful for troubleshooting Mail, Calendar and Collaboration tools.