Thanks for the summary, Cuddles. Lot's of interesting stuff I've never heard before. So what are the circumstances that cause a black hole, or is that still up for debate?
Basically the same, only more so. In a burning star, the gravitational attraction is balanced by the heat and photon pressure from the reactions. When fusion stops, this pressure is gone, so the star collapses. When this happens there are several possibilities, depending on how massive the star is, and therefore how strong the gravitational force is.
For fairly light stars, like the Sun, there isn't all that much gravity (relatively speaking). The Fermi exclusion principle says that a certain class of particles (fermions) cannot exist in the same place as each other. This includes most fundamental particles, including electrons. This means that when the star collapses it reaches a point where it can't go any further without forcing electrons into the same place, and therefore it can't collapse any further. This results in a white dwarf, which is composed of normal matter but has no internal reactions and will slowly cool down and fade until it is just a dead lump.
If a star is heavier, the gravitational attraction is enough to overcome the repulsion. The star can collapse further, forcing the electrons to combine with protons, forming neutrons. This results in a body made up almost entirely of neutrons, which are held apart by a similar exclusion principle.
If the star is even heavier than this, even the pressure from the neutrons can't stop the gravitational collapse. Since escape velocity depends on the density of an object, as the collapse progresses it will reach a point where the escape velocity within a certain radius is greater than the speed of light, and we have a black hole. There are countless theories about what excatly happens after this point is reached and what really happens to the matter inside, but at the moment it is essentially impossible to tell.
There is also a recent theory that there is a stage in between neutron stars and black holes where the neutrons are broken down to their component quarks and gluons and reach an equilibrium before a black hole is formed. This seems a reasonable theory, but has very little experimental support at the moment. A few objects have been identified as possible quark stars, but further study is required, and I believe at least one has been shown to be just a neutron star.