There's the good old Spider-Man dilemma. A situation where you have to choose whether you save the one person you really, really love, or save loads of people you don't know.
Another good one is; Do you try to save one person's live at the risk of endangering other people's? For example, you and a group of other people are all locked up safe in a building. Another survivor comes running along, chased by a group of zombies and he's screaming, "Let me in! Let me in!" You can open the gates and save him, but if you do, you run the risk of a zombie getting in before you can close the gate again. So, you either try and save the guy and endanger the lives of everyone inside, or you just do nothing and let him die.
Also there's a good one from Walking Dead where you don't have enough food for everyone and you need to choose who gets to eat. On the one hand, the moral thing to do would be to feed the children first. On the other hand, the adults are the ones doing all the work, so they need to keep their strength up. Which is more important?