Nothing is completely safe, not even traditional banks. FDIC insurance has many limits and restrictions (eg. it does not cover safe deposit boxes). In 2014 the national bank in Bulgaria had a catastrophic bank run who left depositors like you and me unable to access their money (to this day they still don't have their money - http://www.forbes.com/sites/francescoppola/2014/08/18/the-bu...). In 2013 customers of the bank of Cyprus lost between 50% and 100% of their deposits over 100 000 euros (http://www.bloomberg.com/news/2013-07-30/cyprus-sets-levy-on...). And so on. It is a good reminder that a crisis causing you to lose money can happen at ANY financial institution. Every year there are millions of people losing money who thought was "safe".
That's why it is always a good advice to diversify, to not keep all your eggs in one basket, etc. Bitcoin is no exception.
With that said, it is fair to remark that Coinbase is still probably one of the safest places to keep your coins "online" for day to day usage.