Add me to the "green screen after prolonged inactivity (e.g. overnight)" club. My experiences are similar to many of those described here. I learned that I could disconnect and reconnect the HDMI at the Roku to get it working again. This seems to fix the problem quickly but is still a significant nuisance. Since my Roku XD/S (purchased in December 2010 so that I conclude this is still a problem for new boxes) is connected through an HDMI switch, next time I plan to try simply switching away from the Roku followed by switching back.
Even if Roku can't fix the issue easily, it seems that they could at least put something about it in the user guide and/or the"Ask a Question" on the support page. I didn't find anything in the user guide. I just searched for "green" at http://support.roku.com/home
and found the text quoted below which does not seem to be directly related to the inactivity green screen.
If you see a blue or green screen, try this:
On both your Roku player and your TV or receiver, unplug each end of the connectors and plug them back in again, pushing them firmly, all the way in. Try viewing the video again. Sometimes, the blue or green screens are the result of a loose connector.
If you continue to see only a blue or green screen, your TV or receiver may not support HDCP (a copy-protect method) over HDMI. This is generally true for older TV models that have early HDMI implementations that do not follow current standards. Try connecting your player with another cable, such as a component cable."