PlayStation 4's launch has been going pretty well as far as sales go, but there are a number of systems have arrived DOA. The so-called "Blue Light of Death" has been attributed in a variety of symptoms, and Sony has issued a troubleshooting guide for the error.
The PlayStation Support forums (via Joystiq) lists potential signs like "blue indicator light blinking" and "console powering off after blinking blue." All in all, the error seems to render the console unusable, at least for the time being.
The guide suggests possible causes like TV compatibility, issues with the power supply, or hard drive issues. It recommends a different troubleshooting approach for each potential cause, so you'll have to run through them all to rule out all the possibilities. If that doesn't work, Sony recommends using its Live Chat to speak with a representative.
It's hard to say just how widespread the error is at this point. While the Internet-coined nickname invokes the infamous Xbox 360 "Red Ring" error, Sony has already admitted to a 0.4% failure rate. That would be 4,000 of the million sold so far, assuming Sony's pre-launch estimate is accurate, of course.