So, it turns out there's a name for it: PROSOPAGNOSIA, the inability to recognize faces.
For most of my life, I've had the problem that when I met somebody, I wouldn't be able to recognize them again the next time I saw them, even if it was the next day or only an hour later. I remembered them of course, but I couldn't tell who they were by what they looked like unless there was something striking about them (an unusual outfit or odd hairdo). This is not a problem with people I know well, but only those I've just been introduced to or do not see on a regular basis. It's not a problem of memory per se, since I can often remember specific conversations I've had with someone I don't recognize ("oh, so that was you?"), even if it's been years since I've last seen them (for example, at GenCon or MythCon), but might pass right by them in the halls.
Well, thanks to a piece in the current FUNNY TIMES, I just found out that some other people have the same problem. I don't have the extreme form, which is usually brought on by a head injury (as in the famous case described by Oliver Sacks), for which I'm grateful. It's something I can work around -- though I used to have terrible time recognizing my students when they weren't sitting in their usual seats -- but it'd be better not to have to. At least I now know how lucky I am to have such a mild form of it.
UPDATE: With a little more checking, I see that what I have is more properly called "Congenital prosopamnesia". It's not that I don't recognize a face, it's more that it doesn't get stored in my long-term memory. In my case, this applies to names as well; I can rarely connect the names with the faces of people I've just been introduced to. Since I've had it since at least the third grade (I remember looking around trying to find the people I'd been playing with at the last recess but not being able to identify them), it's not a sign of senile decay but just the way my mind works. Or, in this specific case, doesn't quite work in the way you'd expect it to.