So… I updated the few plugins I use here, all of which say they were tested with the current WordPress version. The anti-spam plugin I use crashed WordPress. Oh good. I removed that and got the blog back (not that anyone would have noticed it missing!) without the anti-spam measures and have now received one (so far) spam post. I can live with that.
Update: The plugin has been updated so that it no longer crashes WordPress. However, it no longer even works at all! Oh well… can’t complain about stuff that is free!