Some users with the new iPhone 5s are getting a very Windows-like 'blue screen of death'. There have been several reports on the Apple support boards talking about it, and even a sample video.
It seems the problem arises when using the iWork apps: Pages, Numbers and Keynote. Reports say the problem happens when the Home button gets a double tap to exit an iWork app. The result, in some cases, is a blue screen and then a reboot of the phone.
I could not duplicate the problem with any of the iWork apps on my 5s, but it's clear some users are experiencing this frustrating bug.