How do we make our multiplayer spawn area less of a disaster zone?

In the standard Minecraft server, the area around the world spawn point cannot be modified by players that are not ops. To work on the spawn area, be an operator ("opyourname" at the console, "/opyourname" in chat by another operator).

You can also change the radius of the protected area in the server.properties file by adding/changing the spawn-protection field, which defaults to 16, that meaning all blocks within 16 blocks of the central column of the spawn area. For example,

spawn-protection=0

will protect only the single column of blocks at the center of the spawn area (it is not possible to eliminate the protection entirely).

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For your particular problem, I would suggest not just fixing the damage but building a safe area around the spawn — that is, well-illuminated so that creepers cannot spawn, and enclosed by walls or fences so that they cannot wander in.

If you're using Craftbukkit, go into your server.properties file, find spawn-protection=1 then change it to 0.