My problem is now resolved. After working on it for more than two WEEKS and trying ever single suggestion in this thread, including replacing the phone, I got it to work (Verizon iPhone 4S, iOS 5.1.1).
I literally spent hours on the phone with Verizon and Apple with no luck. But, during this same time frame, I upgraded my daughter's iPhone 4 to a 4S. When I did this, the problem also appeared on her phone. This fact along with too many others to list here convinced me without a doubt that this is a carrier/apple issue, not a phone issue.
In setting up her new phone, I noticed that MY cell number was associated with my daughter's apple ID. This initially made since to me since I pay her bills for both the phone and her iCloud subscription. However, given the problems, I removed my cell number from her apple account and entered hers. I then changed my Apple ID password and hers. I then did a hard reset on boths phones and attempted iMessage activation on both phones. The first attempt failed, but after 24 hours I tried again and both phones activated for iMessage and FaceTime verifying both the e-mail addresses and the phone numbers (e-mail addresses always verified).
This issue is clearly a problem between the carriers out there and the apple server. Apparently, there is not enough outcry to warrent a full investigation and permanent soloution from apple and their approved carriers.
So, my only additional suggestion is to make certain your cell number is not associated with any other Apple ID's. Check your spouse's account, your children's and so on..... Then change your Apple ID password and try again over the next 24 hours allowing time for the servers to update.