Need a dock/cable that can charge through AC while connected to USB
Solution 1:
I have an old Belkin TuneSync Charging dock, which also is a 5-port powered USB hub, that does the trick. The specs don't say that it works with iPhones, but mine worked just fine with both my iPhone 3G and now with my iPhone 4. I think the spec was just written before iPhones were available, as the unit was introduced back in 2005.
Belkin doesn't seem to still be making them, but they are still readily available. I just found it via Amazon:
http://www.amazon.com/Belkin-TuneSync-Charging-Dock-White/dp/B000BMVIQ2