Above, visual proof that I've managed to get my iPhone 3G activated, syncing, and restoring. How'd I do it? I followed the advice of our genius commenters, of course. Here's the deal:
Short version: Nice people wait, mean people spam the refresh but get it done.
Long version: Hook your iPhone up to iTunes, watch iTunes try and fail to get to the iTunes Store for activation. At this point, you have a decision. The Yin in you will tell you that the reason that so many people are having problems is that so many people are doing exactly what you're doing. So relax, go grab a coffee, and try later. The Yang in you will tell you that, screw those other people, you just need to keep trying until you get through. The fastest way to do that is not to unplug the iPhone but simply to just click OK on the error message, click on another section of iTunes (like a playlist) and then click on the iPhone in the sidebar again.
Or do a mix of the above, the Yin and the Yang, the spam refresh and the sit it out, with little dots of the other mixed into each. So Taoist of you, Steve Jobs would be proud.
Good luck everybody, let us know how it's working for you in the comments! Namaste