Xvnc! I have an Xvnc server running on my otherwise-headless home server right now. I did have to edit the login-manager's settings to run the server properly, but it works, and gives me both 1) a user login prompt and 2) a reconnectable session. It does not provide direct access to graphics hardware, so it can't take advantage of hardware accelerations, nor does it provide for XDMCP or local console logins (as far as I know). But it's ideal for a remote-only X server.
In a typical Ubuntu desktop installation, GNOME comes preconfigured with a VNC server called
Vino that provides a reconnectable remote-desktop, but you do have to login to your console to activate it (Vino doesn't run with
gdm, so it doesn't provide the login prompt). You can enable Vino in GNOME's "remote desktop" settings.
Typical X/XDMCP sessions don't provide this functionality, but NoMachine NX may also enable what you're looking for. You can also use
x11vnc to access an already-running remote X session (similar to Vino).