Accidents can happen, but they are rare. There are two kinds of accidents:
- "contamination" accidents
- irradiation accidents.
If you are *irradiated* then you can be lethally affected and die of radiation sickness in the coming days, weeks or months, but you are not a radiation hazard yourself.
For instance, the three operators which made the mistake at the Tokai Mura plant in 1999
(see
http://en.wikipedia.org/wiki/Tokaimura_nuclear_accident for some info) made by accident a "nuclear reactor in a vessel" (that's a criticality accident), and got very very seriously irradiated (some died), but they were not a radioactive hazard themselves. During the few seconds of exposure, their cell materials were damaged by the ionizing radiation, and that was the cause of their sickness (and eventual death). But they weren't a problem to their environment, radiation-wise.
If you are *contaminated*, that means that on or in your body, you carry radioactive substances of significance. They will irradiate you, and depending on the kind of radiation, your surroundings. If it are alpha emitters (like plutonium) then the radiation will not leave your body (alpha radiation only travels a few micrometers in matter). But it will do a lot of damage locally. The most typical case of alpha contamination is the breathing of air containing powder or so of an alpha emitter, and the exposed area is the lungs.
Now, unless you have taken in A LOT of stuff, you are not an immediate radiation hazard for your environment, however, you might be considered a "leaky container" of radioactive material, and be an indirect hazard because you are essentially a "vessel from which radioactive material might escape".
If you have taken in a hard gamma emitter (cobalt or something), then you ARE a radiation hazard to your environment, because the radiation can leave your body. You are a walking source of radiation, and if you stand close to somebody, that person takes a comparable dose as you do (but only during the time he's near you, while you take it all the time of course). You are also a "leaky container".
For instance, after the SL-1 accident (see
http://en.wikipedia.org/wiki/SL-1 for some info), the people exposed we so terribly contaminated, that one had to consider their bodies as "radioactive waste". But that's because they had reactor core material all over them.
The hazard is only there as long as the radioactive material is there, so if by radioactive decay, it has disappeared after a while, it is gone (but you have taken the dose nevertheless, and hence increased your chances of getting a cancer or so, because of the genetic modifications that it induced).
It all depends on the material you absorbed, the nature of the radiation it emits, and of course the quantity you absorbed.