Alice and Bob's crush Suppose Alice and Bob both want to determine whether the other has a crush on him/her, but they only wish to share the information if the crush is mutual. Is there a cryptographic protocol that makes this possible without using trusted third parties? It is safe to assume that they will not lie during their "encrypted announcement" to the other.
Covert two-party/multi-party computation provides exactly what you're looking for.  The two-party case was introduced by von Ahn, Hopper, and Langford, and a more formal definition and multi-party protocol was given by Chandran, Goyal, Ostrovsky and Sahai.

Covert secure computation even hides whether or not the parties participated in the computation at all, unless the result of the computation determines that it should be revealed.  For Alice and Bob, their inputs would be one bit each, indicating whether each is romantically interested in the other, and the function to be computed on these bits is AND.  If the function output is 1, then that fact is revealed to both of them and they live happily ever after.  Otherwise, they don't even learn whether the other even played the protocol.  So if Bob likes Alice but not vice-versa, Alice won't even learn that Bob participated at all, thus saving him from eternal embarrassment in her presence.

The von Ahn et al paper gives many more applications of the concept, e.g., two undercover spies from allied countries who may want to collaborate.