Once again I feel the need to delurk because there is just too much incorrect information.
First, China is mostly divided into provinces, but some large cities have the same legal and administrative status as provinces. For the sake of simplicity and clarity, let's refer to all of them as regions in China.
There are several dimensions to the Hukou system. One is the so-called rural versus urban divide. Actually in Chinese they are not called rural and urban, but rural and non-rural. This is being phased out. Already a number of regions do not have different registrations for rural and non-rural people. It's all just local resident registration. By 2020 this will no long exist.
Then there's the local versus non-local issue. No, the system does not legally restrict people from moving from one region to another. And no, it does not prevent one's child from going to school, or prevent one from seeking medical attention, and so on. While there are many factors, it's mainly about benefits. A person with a non-local registration does not get all the benefits a local resident does, and a lot of things are therefore more expensive. This provides a disincentive for people who want to move, mostly from more rural to more urban regions. Only the most motivated would try, and only the most qualified and capable will get to stay. As a result, urbanization in China is behind its general economic development. At the same time, urban poverty is also lower than it otherwise would be. This is actually an explicit goal of the system, and one major argument that the system, at least in some form, should be preserved, at least for some time.
The system is being changed. There are many aspects to this. One is to make changing one's registration easier. In some ways this has been going on for more than two decades now. One example is the so-called Blue Seal registration of some regions. Hukou reform is something that's being actively debated in China today, has been for some time. Opinions range from preserving the system mostly as is, to changing it in key aspects, to replacing it with a completely new system. As usual, the changes are incremental, gradual, and slower than many would like, but, at the same time, it's also mostly in the right direction.
Finally, please do not rely entirely on the English wikipedia article. It is not incorrect, but incomplete and at least slightly biased. Those who can read Chinese should really read the Chinese version.
中华人民共和国户籍制度
P.S. A thankyou to the mods for keeping things sane.