A Morton's Fork is a specious piece of reasoning in which contradictory arguments lead to the same (unpleasant) conclusion. It is said to originate with the collecting of taxes by John Morton, Archbishop of Canterbury in the late 15th century, who held that a man living modestly must be saving money and could therefore afford taxes, whereas if he was living extravagantly then he was obviously rich and could still afford them.
See more at http://en.wikipedia.org/wiki/Morton's_fork
A character is presented two alternatives, A and B. If the character chooses A, then something bad happens. If they choose B, a similar or identical bad thing happens — but for a different reason. The Many Questions Fallacy is often a form of this, where a loaded question ("Have you stopped beating your wife lately?") precludes a "safe" answer (since, in this case, by deigning to answer the question, you are essentially admitting that suspicions about you beating your wife are legitimate).
Also see mentioned Hobson's choice, Xanatos Gambit, Sadistic Choice, Contrast Sweet and Sour Grapes, etc, etc