A situation in which there is no possible way to succeed. Usually not favorable, as winning is generally a good thing. Most often, one finds him or herself in a no-win situation after an innocent act that gets blown out of proportion.
Some examples would be:
Trying to have a nice discussion with extremists on their topic of interest.
Arguing semantics of rules with parents.
Getting caught in a risqué looking position accidentally and trying to convince someone that you were not doing something wrong.
Jokingly admitting something about yourself and having people believe it.