I created a Windows service to monitor a web application and its database; it retrieves the application login page and also connects to the database and runs a query that is commonly used in the application. If an error occurs on the web server side, it will notify the server hosting team about the problem. For SQL Server errors, it will notify the DBA team and if the error is "Path not found" or other network related error, it will also notify the server hosting team. I added checking on when the application's security certificate will expire and it sends notifications a week from expiration. It would be nice to have the certificate expire outside of the hurricane season, but it expires during the height of hurricane season.
It's not as fancy as the Stack Overflow monitoring, but it found when the security certificate expired last year.