OK, I'm feeling really stupid. I managed to change my exim .forward file [which filters my e-mail neatly into a lot of mail folders] in such a way that it doesn't deliver e-mail _at all_. Ouch. Such a stupid typo. Well, two of them. I hope these messages are still drifting somewhere in the mail subsystem and get delivered after all, because there are some very important ones among them. Gah.
W00t, just for the record: run exim -qqff as root, and you're just fine :D