Xpra: Screen for X
xpra.org
xpra.org
For me, I'm using it primarily as a way to run Pidgin (for Jabber and AIM, primarily) on my server that I can connect to from the various machines I use around the house; analogous to how I use irssi in screen for IRC.
I also configured my screen instance to have a DISPLAY environment variable that corresponds to my Xpra instance, so if I run anything within screen that connects to an X server, I can be sure it's connecting to the X server I'm currently connected to anyway, and I'm mostly safe from sudden disconnection problems.
Now wherever I need to use the program(s), I only need to re-attach the Xpra session, and it shows up at the local display. This allows me to keep the same windows open, but I'm taking them with me, wherever I go. Also, the programs keep running when I close the connection (or when it drops), so I don't have to a) start them again, or b) restore state.
More Xpra goodness: allows me to change the compression and algorithm on-the-fly; is more responsible than SSH X forward on slow/laggy connections; has a "connection problem" visual indication (the windows are overlaid with a spinner, instead of just freezing).
I stand by my statement that xpra has only a "rootless" mode, but I will agree that with Xephyr (which is a less-sucky Xnest), there is less of a difference anymore.