It depends on the computer. Some (generally newer) USB ports can provide enough power to support the current draw the iPad needs to charge, but older ones have a lower current rating that doesn't necessarily support the iPad. It looks like the iPad will say "not charging" if connected to a USB port that doesn't have the specs to support, even if the iPad is actually charging, though at a slower rate.
It's similar to the "bricks" Apple provides for charging. The smaller iPhone "cube" is rated at 5W (as I recall), and the larger one supplied with the iPad is 10W. I plug my iPad into the iPhone charger fairly often and it does charge, but I think it's slower than the 10W iPad charger.