The backstory (as I seem to always have to include in my posts): I was a huge Ultima 6 fan. At the beginning of that game you created your character via a series of ethical choices. None of the choices was obviously wrong; there were "right reasons" to do every single one. It wasn't a matter of choosing, say, greed versus charity; it was a matter of deciding whether you preferred charity or honesty. To give an example of that exact conflict:
"You are walking down a street in the poor part of town, littered with beggars. Walking in front of you is an obviously rich gentleman. His change purse has fallen out of his pocket, but he does not seem to have noticed. Do you...
A: Pick it up and return it to him, as honesty compels you to do?
B: Let the beggars keep it, as the rich man will scarcely notice the loss?"
Given no further information or assumptions about the rich man or the beggars, both options are pretty valid choices for someone of good morals. It's just a question of which way you lean. I seem to be relatively bad at making up such things myself, especially on the fly. Given some of the games I've seen from folks here, I'm betting you folks are pretty good at it.
So that's the challenge: write a quick moral dilemma, something that pits one moral right against another, where neither choice would be obviously wrong. Something that you don't solve via logic or examination, but by a sense of virtues.
No-wins and quandaries are also acceptable.