There's a lot of speculation and science fiction devoted to the idea of what may happen when a person falls into a black hole. I don't know all the physics of a rotating black hole, but it is impossible to fall into a nonrotating one (even if the person were to survive the radiation and tidal effects, and other hazards mentioned by Gorgonzola). The reason is quite simple: It takes a (theoretically) infinite amount of time, as measured by an 'external' observer, for any object to reach the event horizon (as mentioned by viper281). However - black holes do not exist for an infinite amount of time. Hawking radiation causes them to evaporate.
As viewed from outside, a person falling towards a nonrotating black hole will appear to slow down. The watch on the faller's wrist will appear to tick slower and slower. The faller will never touch the event horizon, and if the observer keeps watching on long enough time frames, the hole will shrink. What happens when the event horizon radius reaches zero, I don't know (some claim a naked singularity).
As viewed by the faller, the watch on the external viewer's wrist will appear to tick faster and faster as the event horizon approaches. The same Hawking radiation that the external observer sees, the faller will also see, only at a much much faster rate because of gravitational time dilation. The time dilation will always work to shrink the black hole to nothing before the faller has 'time' to hit it.
This idea has an important consequence in considering the formation of (nonrotating) black holes: that is, they never fully form at all! The outermost layer of a collapsing star will fall towards the event horizon - but will never get there. There will never be a black hole in which all the mass is within the event horizon radius, because the mass has to fall in from someplace outside of that radius, and anything outside never finishes falling in. One might make quantum theory arguments about how all the mass can get inside the event horizon, but to the best of my knowledge, current quantum theory is not applicable at the limits of gravitational effects. In other words, where BlakJak says "The occurence of black holes is a result of a star's state of collapse causing it to be smaller than its own Schwarzschild radius", the time dilation experienced by the outer shell combined with the Hawking radiation actually prevents that state from ever really happening.
One more thing worth noting: Every massive object has a Schwartzschild radius. An electron has a Schwartzschild radius. The Earth has a Schwartzschild radius. However, the radius of the Earth is greater than it's Schwartzschild radius, which is why we're not living on/in a black hole.
I just realised, I'm not sure if the black hole I describe in my writeup needs to be electrically neutral too. A charged black hole may have extra properties which cause even further complications. For the sake of simplicity, pretend I've been writing about a neutral black hole all along.