I've found some related answers: I think I get maps and worlds, and I now know where single-player saves are located. I'm not sure I completely understand this answer about copying a multiplayer map to single-player, but in any case, I'm only concerned about multiplayer survival mode:
Suppose I'm running a Minecraft server on Windows for myself and friends. Which files should I save to "back up" the state of the world at a particular point?
For example, I might want to do this just when I need to shut off the server, to be sure not to lose anything; to save one world and go back to it later, while starting a new one for now; or to restore the world from an earlier state, when we hadn't flooded the house with lava yet.