Solution 1:

I actually found a way to accomplish this. You are still signed in with your Live account in all the other services, but not in Messenger. Other people will also see you as offline, but you can be online on other instances (e.g. your other computer) without interferences (you will be shown and seen online there).

Open the Messages App, go to the upper or lower right-hand corner and wait till the overhead menu appears. Choose "Settings" from here. You will be presented with some settings, choose "Options" (I only have the German version, I suppose it reads Options in English). There is only one settings, it should read something like "Send/receive messages". Turn this setting off and you will be offline in MSN on Windows 8.

Side effect: You will also be signed out of other messaging services in the Messaging app, but because (for now) it only supports Facebook, this shouldn't be much of an issue.

Solution 2:

Do you have the Messaging app installed? Try going there, pull up the command bar, and change your status to "Appear offline". Or, just uninstall Messaging (but this will also uninstall People, Mail, Calendar).

Solution 3:

  1. Go to right bottom corner.
  2. Then Settings
  3. Account
  4. Click the account, e.g. Hotmail
  5. Scroll down and you can see Remove all accounts .
  6. Click it once and then once again – now you are logged out.