I had the same issue on 2 iphone 5, 1 iphone 4S, ipad 2 and ipad mini...
I tried ALL the fixes available all over the internet.
I figured if i was not the only one, then it surely isn't a local problem, so i might as well wait for a while as probably every ios device owner is upgrading and apple servers must be getting hammered.
after 4 hours, activation failed!!
Tapped imessage and facetime off and on again. they activated both in under 20 seconds.
all is back to normal on all devices.
so just give it some time.
PS. everytime you off/on imess and facetime, you restart the process. Once on, don't off it.