First, the AT&T servers were overwhelmed, preventing access to existing accounts and blocking people from creating new accounts or whatever changes were necessary to set up an account with the 3G iPhone. If this first step was successful, then you moved to step No. 2: Authentication via the iTunes server.
The first step took time, and often had to be repeated before things would go through. Eventually, however, it worked for me.
Step two was (and still is) a problem. The iTunes server continues to struggle with the onslaught of requests and can't be reached. In the end, after several unsuccessful activation attempts, Apple allowed me to walk away with an unactivated phone. The representatives at the Apple Store told me to continue to try to authenticate it through the iTunes server once I got home.
I've been trying for 30 minutes now with no luck. So I have an iBrick that can only make emergency calls. My old iPhone already has been deactivated, and can no longer make or receive calls.
Hopefully the iTunes server will respond and let me activate the phone at some point...