The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.
The Minecraft client can be played offline as long as the game has been connected to the internet and authenticated once. Unless that's changed in the past few months.
The server can now be started in either online/secure mode or offline/insecure mode. A secure server requires all connecting players to first authenticate on www.minecraft.net, then checks that the authentication matches, before letting the player in. A server running in offline mode won’t do any such checks, nor will it ask the client to authenticate, but you can’t be sure that people who connect really are who they claim they are. Offline mode is meant for LAN plan where you know the people connecting to the server.
So it sounds like if you're running the server in insecure mode, you'll have a harder time dealing with trolls.
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Notch added an offline mode to the server in August. Server versions >= 0.1.1 should work.
So it sounds like if you're running the server in insecure mode, you'll have a harder time dealing with trolls.