It looks like the first-day demand for the iPhone 3G may have brought down a critical part of the iTunes Store. After you get an activated iPhone, you still must synch it with iTunes before you can use it.
My attempt to do the initial sync on both a Mac and a Windows machine failed. Windows reported a timeout error trying to connect to the iTunes store, while the Mac just sat there forever saying “Connecting to iTunes Store.”
An attempt to sync an iPod Touch generated the error message above.
I’ve reported the problem to Apple and they’re checking it out. I’ll update when there’s news.