E.g., for rolling daily backups, something like
ls -l *.backup | mail -s "backup done" me@foo.dk, someoneelse@bar.dk
even for successful cron jobs. That way you can check file sizes, timestamps, etc.
That way I will notice if something is not working, even if emails are also not working, the server is down etc. It requires of course that you actually read those emails. But at least if people have accepted to check them, they cannot complain. Well, they can of course, but then I can also blame them.