Ken Shirriff has done a great job of comparing a counterfeit iPad power adapter to a genuine Apple adapter over at his blog. The teardown revealed that most of the time, the counterfeit chargers are a 5 watt charger instead of a 10, are poorly constructed, and have major safety issues. The chargers look identical to each other than small differences in text. For instance, the real charger says "Designed by Apple in California" while the fake one does not.
The Apple charger has much more insulation. The upper (high-voltage) half is wrapped in yellow insulating tape. Some components are encased in shrink tubing, there are plastic insulators between some components, and some wires have extra insulation. The counterfeit charger only has minimal insulation.
The build quality of the Apple charger is much higher. In the counterfeit charger, some components are visibly crooked or askew. While this doesn't affect the circuit electrically, it indicates a lack of care in construction.
Flipping the boards over reveals that the circuitry of the genuine Apple charger is much more complex than the counterfeit. The Apple board is crammed with tiny surface-mounted components in every available spot. The counterfeit board has a lot of empty space, with just a few components. Note the reddish insulating tape in the lower center of the Apple board, another safety feature of the genuine charger.
Last year, Apple launched a USB Power Adapter takeback program which was an effort to help replace counterfeit chargers with real ones, after a few deaths occurred because of the chargers.
You can also check out his iPhone charger teardown here