My wife and I just got iPhone 5's, and had trouble activating both. We followed the setup steps, connected to our home WiFi, and did the full process, but the phone didn't activate. Instead, we kept getting a "This phone is not activated" message. On her phone (which arrived a day earlier) we called Verizon support, went through a lot of steps, then got transferred to a "level 2 tech". However, just as he was looking at our records, the phone started working. The explanation given was that sometimes it just takes a while for the system to update.
When my phone arrived, I again went through the activation process, then waited several hours. No luck, the phone still wasn't activated, so I called Verizon support. I was lucky enough to get a fellow who said he'd been answering iPhone questions all week and had a possible solution to the problem.
"Just turn the phone OFF, wait a couple of minutes, then turn it ON again."
I did as he instructed. About a minute after I turned the phone back on, I got the message "Activating your phone", then a minute later "Your phone is now activated."
Maybe this was a unique situation, but I wanted to share this information with everyone in the hopes of saving folks some time and aggravation.