After a few nights sleeping on the porch (in subfreezing weather), we decided it was reasonable to assume the neighborhood cat was actually a stray, rather than someone's outside cat. Took it to the vet Monday, found out that "it" is actually a "she." She's between 1 and 2 years old, a medium-haired muted tortie, and a little under 7 pounds. She had an ear infection and roundworms, but nothing more serious; the vet thinks she hasn't been fixed, though. (And there's a slight possibility she's pregnant, but hopefully not.)
So she got her shots, got ear drops and ear wash and some skin stuff for the roundworms and pills for fleas (just in case - although she doesn't appear to have fleas). She didn't care for the ride to or from the vet's, but she was just fine during the visit itself - made friends with the tech, assistant, and the vet. Need to make follow-up appointments to complete her vaccinations and get her spayed.
We're running a "found cat" ad in the paper for the next few days - the paper lets you do that free, which is nice - but I honestly don't think it's likely that anyone will call. She's been in the house for 2 days, effectively living on our porch for several days before that, and nobody seems to have missed her. There are no "lost cat" signs up, nobody asking around, zilch. Ah well.
But I suppose the silver lining is little Miss J herself (provisional name is Jezebel, a sort of backhanded reference to just how calm and well-behaved she has been). She stayed shut up in the downstairs bathroom until she proved she knew how to use a litterbox (and, coincidentally, until we had cat-proofed the common areas of the house). Since then, she alternately follows us around or curls up in odd corners; after a little coaxing she did play with one of the toys we got her. And last night she let me trim all her front claws on the first try, which I think is remarkable.
So far, we can't get any real nice pictures; but as soon as we've got some, expect to see far more of a little gray cat than you ever thought you needed to see.... :-)