Luckily we turned the water off before it spread out of the bathroom, and the drain in the floor got most of the water, but enough still managed to seep through and run down the walls downstairs (this is a pretty old house). Not great.
Luckily it happened with all of us at home and awake; several hours earlier, and we'd have been at work, and a few hours later and we'd be asleep.
The plumber's already been contacted and he's coming tomorrow morning, but...no toilet or shower until it's fixed.