Protect Beaglebone Black from Power Outage
@jippie is right. the issue is the filesystem. If your OS is actively writing  at the point when power is lost then you have the potential for issues. The risk is lower if the system is not heavily used and the frequency of power outages is low. But it is still there.
The best defense is to provide a battery backup that can run your BBB for a few minutes and get the  BBB to monitor the input power. As soon as it drops initate a controlled shutdown.
This is essentially what commercial Uninteruptable Power Supplies do. So you can eother roll your own or choose a UPS with a linux agent and use that.