A possible game would run like this: Player A is Richard the Lion Heart, Player B is Thomas A'Beckett and Player C is Genghis Kahn. Player A is first and asks "Am I Male?", the rest of the room says "yes". Player A gets another go and so asks "Am I a warrior", and gets another yes. Player A's next question is "Did I speak English?" to which he finally receives an answer of "no". Player B's turn is next, so she asks "Am I male?", to which she receives a "yes". Her next question is "Am I a religious figure?", to which the answer is "yes", she then asks "Was I murdered by two drunken French knights?", to which she also gets a "yes". At this stage she decides to guess "Am I Martin Luther", which receives a "no". The third player asks "Am I female", which receives a "no", so the turn rotates back to the first player, and the game continues as before.
Although the example of gameplay I gave was rather silly it did highlight one possible difficulty. Richard the Lionheart never learnt to speak English, but this is not necessarily a well known fact. In an ensuing argument about wether or not Richard spoke English all sorts of clues could be given away (he was king of England, he only spent five months in England, he spent most of his time on Crusade), making it very easy for the person with Richard on his head to guess who he was next time.
One way to overcome this difficulty is to appoint an arbiter (preferably well versed in these sorts of things) to make a quick decision whenever there is contention. Another is just to make sure whoever writes the names knows enough about them to give an answer that has a high probability of being right.
Another problem that can occur is when a question is asked as a negative, for example "Am I not English?" will probably be answered as "yes" even if the person in question is English. This may be viewed as a result of people not being logical enough in their comprehension of language, but it does occur a lot, and so it is best to mention before the game starts that in the above example the correct response would be "No, you are English".
You may wish to take the winners from each game and play them off in a "final".