So I log in just now and no new mail. That's odd - just the normal system cron jobs give me a couple of dozen messages a night.
My boss looks after the mail system (postfix, with generous doses of amavis, clam, and spamassasin). And he goes skiing abroad for Christmas. So if it's going to be fixed it's going to be me. I've just been landed in it!
(Tracked it down to a typo in the amavisd config file. Would have been alright if it hadn't fallen over and failed to restart. So I roll back a version and everything recovers.)