I came across a simple problem recently. Users setup alerts to a list (announcements). When they setup alerts, they get an automated email confirming the setup. But when new announcements are added to the list, users do not get alerts by email.
In the farm, I had 3 servers with different responsibilities. Then I noticed on the Timer Status 1 of the serves had failed. I spun to action, went into each server and restarted the Windows SharePoints Services Timer. This fixed the problem and alerts started coming through.