I know you've said a headless pc is pretty unlikely, but I thought I'd explain what RDC and VNC do anyway...
I haven't used RDC... but as far as I know it works pretty much the same as VNC, so I'll just mention VNC here, but it pretty much applies to all these type of programs...
With VNC you install the program (the Server) onto the 'headless' PC and use the Client program on the PC you want to access it from (with VNC you could connect from two computers at the same time if you wanted... you'd just be fighting for the mouse - always fun that :] ). VNC displays a window on your screen that's a replica of the desktop on the other machine, and transfers your mouse and keyboard commands within that window to the other PC... so essentially it's the same as sitting at that machine, just from a distance.
VNC can also come in handy in quite a few other situations... the machine doesn't have to be a 'headless' one... you could just be lazy and not want to walk into the bedroom to control that machine (eg. You want to access a directory on the machine in the other room, but haven't shared it yet... just VNC in and share it without moving from your seat :] )
VNC can also be set up to make two computers seem a little more like one. Put the two computers monitors next to each other and using Win-VNC you can set it up so that when you move the mouse to the edge of computer 1's screen (the computer that the mouse is attached to) the cursor will appear on computer 2's screen and control that computer. Just move the mouse back to computer 1's monitor to control that one... this makes it seem like one computer with an extended desktop, but you get the benifit of having two distinct CPU's (eg if one crashes, the other will still be running).
Anyway, that's just some of the fun one can have with desktop remote control programs :)
If you have any questions, just let me know :)