Talking about the case of Alexander Litvinenko... If I remember correctly, he was poisoned with a substance emitting alpha particles. The truly ingenious part of it is that you could carry said substance - it was polonium-210 - in a little tupper box with you, and nobody would be contaminated. And since the substance was ingested (and the human body obviously doesn't have any way to get rid of it again), it could harm the body from within - without emitting any radiation out of the body. (Remember, alpha particles can't get through any solid matter - not even a sheet of paper.) The problem is that the substance used took its time to actually kill Mr. Litvinenko. The most obvious change in his body was the loss of his hair, I think.
You might also want to look at this link:
http://en.wikipedia.org/wiki/Radiation_poisoning#Internal
