One of my servers wasn't sending mail. This server is supposed to report by email on its usage each day; it's also supposed to send alerts on various bad situations, should they develop. But it wasn't sending email. Why?
This wasn't an urgent situation, so rather than dive in and try everything possible, I mulled it over. Today, I came up with a possible answer, and when I checked it, I was right.
Sendmail wasn't running. That's why it wasn't sending mail. Duh.
I dimly remember shutting it down temporarily, and I don't remember restarting it. So I restarted it, and I was instantly rewarded with a flood of 100 emails that it's been keeping in its out-tray for the last couple of weeks.