An iPhone charges just fine when plugged into a computer's USB port. The same goes for an iPod, a pocket camcorder, and any of countless other devices. So what's the iPad's problem?
Actually, the difficulty isn't with the iPad, but with the USB port: It's not supplying enough juice. The ports built into most desktops, laptops, and even powered USB hubs don't generate the 10 watts necessary to charge an iPad's battery, which is why the ‘Not Charging' message appears over the battery indicator. That's a definite bummer, as it means you can't use, say, your laptop to recharge your iPad on the road. In fact, Apple recommends finding an AC outlet and using the bundled 10-watt power adapter.
That said, lower-powered USB ports will recharge an iPad--just very, very slowly. When the tablet's screen is off, the battery does indeed draw a trickle of power. Turn the iPad back on, however, and you'll see ‘Not Charging' again. (It's kind of like yanking open the refrigerator door to see if the light is still on.)
You should be aware that many PCs pump varying wattages through different USB ports. Frequently the USB ports at the front of the PC are of lower power than the ones in the back. Before giving up, try moving to another port.
(For more solutions to perplexing PC problems, see "The 21 Greatest PC Mysteries--Solved!")