With launch-day consoles, hardware issues are expected. Every console maker experiences these problems, but this is unfortunate for the consumers affected. If you are one of those people having issues, look at this post to possibly remedy any problems with your PS4.
Unicorn--Justice on the PlayStation forums has posted a troubleshooting guide on how to fix the "Blue Light of Death" and some other issues you might be experiencing. If this guide doesn't help, be sure to contact Sony's customer support. I know waiting on the phone can be frustrating, but patience is a virtue as they say :)