This issue i had it with 15.10 and it's still here after the 16.04 upgrade.
The whole system freezes, no keyboard/mouse input works anymore. I tried a variety of keyboard combinations (found on the internet, like Alt+SysRq+REISUB and others), but none actually worked. The system is completely unresponsive, only a force shutdown works at this point.
Interestingly, i can't correlate this freeze with any specific program or application, as the system hangs sometimes even while doing the simplest operations like opening the Terminal, or the Unity search.
I would be interested if there is any log saved that could contain useful information on these hangs.