Run one? Read this. Don't? Well, go google "cute kittens" instead.
I really need some feedback on this, as it's not something I can easily check. Until now, the Linux Dedicated server has needed all sorts of faffing about with X-11 and... stuff. I've just uploaded a snapshot of the latest codebase into the Tool, and added a new branch there called linux_server_headless - this has had the Unity option 'headless mode' ticked, which should remove all of the X-11 dependencies.
If anyone has the necessary setup to download this branch (remember, it's AppID 443600 ) and let me know how it's behaving!