It would be nice to have a screen saver based on Stellarium. Preferrably, there would be a Windows version and a Linux version. A fixed view (e.g. facing north at 30 degrees up) screen saver would be the easiest for the first version. Future versions could have the view camera slowly pan across the sky.

Just make sure that it does not use 100% CPU and 100% GPU power while the screen saver runs. Capping the framerate based on an optional user setting would be a quick and easy way to limit CPU/GPU usage.