What is a "blue screen"?
Certain Android devices sometimes become unresponsive and display a plain bright blue screen with no text on it. See photo.
What should be done?
(This answer is based on what someone on IRC once told me.)
If you only ever see a blue screen once or twice a month, ignore the problem and restart your phone when it happens.
If you see so many blue screens that it's worth the effort involved in troubleshooting, then it's time to dig for the cause of the problem. Here's how.
First of all, grab a pen and paper, and make a note of the exact time when the blue screen appeared. Hours, minutes, and seconds. This will come in handy if you decide to run
adb logcat later.
If you have adb (the Android Debug Bridge) installed on your computer, and if you have enabled "USB debugging" on your device, then
adb logcat might (or might not) provide you with some clues as to why the problem happened. In fact, I've always found that
adb logcat works fine even while the blue screen is still showing.
(If you aren't using a very recent version of Android, then your logs will lack timestamps. In such a situation, use
adb logcat -v threadtime to show the timestamps.)
If you experience a blue screen and want to make it go away, reboot your device. If you have
adb installed on your computer and working, then open up an
adb shell and reboot the phone the graceful way. If the graceful way doesn't work, choose the semi-graceful way by using the
adb reboot command. If you don't have adb installed, do an unsafe shutdown by holding down your device's power button for ten seconds. If that still doesn't work, pull the battery out.
But why did the blue screen happen?
I don't know.
You should post a separate question. Tell us the hour, minute, and second when the blue screen came up. Provide us with all the log entries (from each of the several logs which
adb logcat dumps out) starting from 30 seconds before the blue screen appeared, right through to 30 seconds after. Let us know approximately how many times the problem has happened. (Dozens in the past year? Hundreds in the past month?) Also, tell us whether or not you have figured out a set of steps to reproduce the problem on demand. Finally, please do provide us with all other relevant details.
What should be done after the device has been restarted?
You should make sure that USB debugging is enabled. This will make sure you can use
adb in the future. For instructions, see the PhoneArena article entitled "How to enable USB debugging on Android". You should only ever have to do this once.
(This is a community wiki answer. Please edit it and improve it. A big thank you goes out to Izzy and eldarerathis for helping to refine things.)