It turns out I didn’t break my WordPress install. But my home IP address *had* changed, and I have lots of things locked down to specific IP addresses for access. So I’ve got two of the three sites puzzled out. But one of them appears to have a broken theme directory. I’ll be looking into that now…
[A few minutes later, after looking at logfiles] Yup – the twentyeleven theme needed fixing on another site – I refreshed the whole thing, and I’ll keep a close eye on it in the next short while. I don’t remember mucking about in there … but it’s possible.