Want to get a better grasp of your protagonist or other character--or yourself? Consider this quote from Carl Jung:
"The shadow is the negative side of the personality, the sum of all those unpleasant qualities we like to hide. ... There is no light without shadow and no psychic wholeness without imperfection."
One of the most revealing questions you can answer about a character is what darkness he or she is trying to hide. It's not necessarily anything they have done, it could be something they are afraid they might do. Of course it's your duty as a writer to throw temptation in their path.
If you are trying to figure out the character arc for your protagonist (the kind of transformation he or she will undergo) a story in which they learn to accept their shadow side usually is worth telling.