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.
Thanks a ton for this advice. I just got back from an overseas trip where I swapped my SIM for a local one on my Verizon iPhone 5 and iMessage wouldn't work. Simply re-activating iMessage didn't fix it, but once I re-applied "My Info" and re-cycled the iMessage activation and Facetime activation, it started working immediately. THANK YOU!