I wanted to have my Pi connected to a big HDMI TV on the other side of the room and control the desktop from a VNC window on another computer. It took me quite a while to find out how to do this, so I'm repeating it here. The secret was to use x11vnc instead of the tightvncserver I started off with. Install it, then store a password as the user you want to have access and it will be in ~/.vnc/passwd
sudo apt-get install x11vnc
Start the GUI on the HDMI first then run the x11vnc from the command line as the same user (either on the main desktop or remotely via ssh).
x11vnc -rfbauth ~/.vnc/passwd -display :0
Then run a VNC client like Real VNC and log in remotely on port :0.
Interestingly enough, it looks like x11vnc runs right alongside tightvncserver, allowing me to have one VNC window on port :0 (x11vnc) going to the HDMI desktop and another on port :1 (tightvncserver) with a new, independent desktop.