Yea, the GUI is what most people think of as "Windows," but it's not.

Server 2008 can be run without the GUI, for example. Since there are definitely similarities between Vista and 2008, I was wondering if it was possible.

Well, I can answer my own question. The option is called "Server Core" and it is available in Server 2008 x86 and x64. For 2008 R2, it is available only for x64.

Looks cool, but no mention of any support for client OS.