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Not all USB ports are powered. It is often necessary to connect certain peripherals directly to a USB 2.0 port on the computer (as opposed to, say, a USB jack on the keyboard itself).
Not only that, but I suspect that the iPad needs a lot of power from a USB port. If the port can't provide enough power, I think the iPad doesn't draw enough to charge itself. I thought that there were power negotiation protocols built into USB for this purpose.
Each USB device has a set of descriptors to describe itself and its supported capabilties. The amount of current required by a device (from the cable) is provided in the configuration descriptor. For example, a device could have two configurations that are exactly the same, only differing by the amount of currented needed from the cable. Host software can determine if the port to which a device is connected can provide 500 ma, and if so, select that configuration which instructs that device that it may draw that amount of current.
That is incorrect. All USB ports are powered, it's just the amount of power available varies. The USB spec says all ports must provide 5V. The second part of your comment is correct.
My mistake. There are USB hubs that are classified as "powered" or "unpowered", but I guess in the unpowered case it's relying on the computer's supply.
It charged fine on my MBP 2009. But only after it was activated through iTunes. (9.1 is crap by the way consistently crashes when trying to play music.)
This is merely an issue of not enough power available from certain ports, not a Mac vs. PC thing. You'll notice one of the ports they tested was on a Mac keyboard. The keyboard is self-powered and has a built-in USB hub for the mouse.

Those ports have less current available because the keyboard, mouse, and hub consume power in addition to whatever the iPad uses. The host machine has to supply power to all of those.

This is why some USB hubs have a power injection connector. It allows them to supply the same current to downstream devices as the host PC.

To put real numbers to this:

The iPad battery stores 25 watthours of energy.

USB 1.0,1.1, and 2.0 devices may draw a maximum of 500mA from the 5v lines of the connector, this is 2.5 watts.

USB 3.0 will up this to 900mA for 4.5 watts, but it isn't here yet.

Actual current available at a port depends on topology. If I plug my keyboard in to my USB 2.0 computer, then plug my iPad into the keyboard it will only be authorized for 400mA, because the keyboard claimed 100mA. 2 watts.

So, best case, charging an iPad from USB 2.0 will take 10 hours, if it is off. Notice this is suspiciously close to the runtime on battery, i.e. a running iPad consumes ~2.5 watts, your whole USB power allotment. Hence you can't charge while running on a stock USB port.

So, what is with the 10 watt charger? Apple, and probably others, got tired of how long it took to charge and have deviated from the USB spec to allow larger charging currents. 1A chargers are common for iPhones, and at least some Macintosh models have higher current USB ports on board.

I don't know how they negotiate the higher current, but a 10 watt charger could theoretically charge your iPad in under 3 hours.

High power mode was added to the 2.0 spec as an addendum only about a year ago as an optional feature. As more devices require high power for charging it's going to be a very confusing situation for consumers. They could have at least bumped the spec to 2.1 to identify high power capable ports.
If it becomes a big deal (pretty likely, now), they'll probably start slapping "High Power!" on systems that pump out more juice. Simple spec or not, if it's a selling point, it will be made known.
Someone should make a little dongle/tester. (A quick search of newegg and monoprice did not suggest one yet exists.)
I think the port reports it to the computer, so you should be able to find some sort of USB utility that will tell you.
A few points to clarify. In USB 2.0 and earlier, there are two kinds of hubs: self-powered and bus-powered. Self-powered hubs must provide 500 ma at each downstream port. Bus-powered hubs must provide 100 ma at each downstream port.

There are also two kinds of devices: high-power and low-power devices, meaning that they consume from their upstream port more than 100 ma or 100 ma or less, respectively.

A bus-powered hub is a high-powered device, as from a port point of view, 500 ma can go down the cable to it (and devices connected to it).

The maximum number of ports that a bus-powered hub can provide is 4 as 400 ma are required for each downstream port and the hub functionality uses some power.

You cannot plug a bus-powered hub (a high power device as it can consume 500 ma from its upstream port) to a bus-powered hub. You can of course alternate between self- and bus-powered hubs.

If the iPad can operate on 100 ma, then it can be connected to a bus-powered hub. If it requires more power, then it must be connected to a self-powered hub.

Hope this helps.

On a historical note, Apple has built systems that provide more than 500 ma from the root (the ports in the system itself). I am not an expert on if they still do. I'd hazard a guess the answer is yes.