Would like to be able to connect to an existing X display, so can access my work environment and everything I left open from home. I vaguely remember something about using x11vnc in the past. But the package does not exists for Fedora 11, so I am thinking there is some built in method now.
NOTE: I connect to my work machine through a VPN so password protection is all I need security wise.
Use x11vnc, It will attach to a running session and let you share the desktop. If you run it as root to connect to an xdm session, you will need to do some research into Xauth as it can be a bit fiddly to set up.
Edit to add: Karl Runge no longer appears to be maintaining the original x11vnc however development is continuing on github. Or you could do as suggested below by @ivan-talalaev and use x0vncserver.
Another advantage of this server is that it supports alot of the advanced VNC features used by UltraVNC including large bitmap caching and file-transfer.
According documentation Tigervnc has support for this.
Make sure
vncserver
isn't already running, or you'll get the errorfailed to bind socket: Address already in use (98)
If you're using KDE at work, KDE already has a VNC server built in.
Presumably, GNOME does too.
As an alternative, you might want to look at NX. It is usually much faster than VNC over the Internet, and I know you can configure it to be able to access the running X session on the console.
x11vnc (http://www.karlrunge.com/x11vnc/)
Use xrfb.
Edit 2022-04-05: xrfb is, no my knowledge, not the same as xvfb. Someone suggested an edit changing this to xvfb, but I think xvfb is not actually an answer to the question of how to VNC into an existing session.
But xrfb no longer exists in debian/ubuntu, it seems, and seems to generally have been disappeared from the Internet.
So my answer was fine 13 years ago, but not a good answer today.
I did a fairly elaborate setup for a customer site that might be appropriate for you.
See the details here.
Beware the security implications too.
VirtScreen may be also interesting option/wrapper , helping in setting up x11vnc with xrandr : https://github.com/kbumsik/VirtScreen
Also: Extending your X11 Desktop using VNC https://ogbe.net/blog/moar_monitors.html