I recently had a problem because of a virtual server. The server was running really, really slowly, and nothing seemed to be causing it, so far as I could see. Turned out that the actual hardware was being slammed by too many I/O requests from other VMs on it, which was affecting the database server, but not visible from it.

The overall load hadn't gotten to the point where automatic alerts would be sent to the sys admins, and even if they had been sent, they wouldn't have come to me.

That kind of thing makes for a whole new level of answers to the common interview questions about how to handle a slow database server.