Crap. Looks like our water heater has sprung an irreparable leak, which means there is an expensive repair in our future. On the good side, the shutoff valve, which is directly above the heater, has been corroded since we moved in, and whose handle snapped off in my hand when I tried to close it, will get replaced too.
Update 2.23.09: Water is back, and life may resume as normal. We got a new AO Smith 50 gallon unit installed with an expansion tank and a new shutoff valve, as well as a gas shutoff (which was never there). Expensive, yes. I did peep out tankless systems, but the entry models at the H-D topped $1K to start, and I’d guess the pro-grade models would be an extra $200 or so before installation.
The funny part of the story is that I got home from a 5-hour Scout adventure Saturday afternoon and decided I’d put some extra time in on the basement while I was still in work clothes. I hadn’t been downstairs more than ten minutes when I noticed the first trickle of water from the heater, which grew into a pool an hour later. If it had been midnight, or a day when Jen didn’t make it downstairs, the whole basement could have been awash and we wouldn’t have known until the dryer floated away.