The Trolley Problem is a thought experiment created by the Oxford philosopher Philippa Foot in the context of the ethics of abortion. Until recently I had never heard of it even though it's well-known among philosophers. This month, the BBC World Service devoted an entire documentary to it called “Would You Kill the Big Guy?” Despite some hokey production choices (including a philosophy-themed gameshow), the two-part series is well worth a listen. I would have been happy to leave the Trolley Problem to professional philosophers except that as I thought about it, I realized that it's not an exaggeration to call it one of the best tools for moral thinking that we have.
The most basic version of the Trolley Problem is this: There is a runaway train hurtling down a track and five unsuspecting workmen are about to be flattened. You notice a junction that could shunt the train onto another track where there is only a single worker. The lever that operates the junction is right next to you. What do you do? Do you allow fate to take its course and the five to die, or do you intervene, pulling the lever and saving the five but directly causing the death of the one? (We assume that there are no other solutions, such as shouting a warning. Since this is a thought experiment, there is no need to add endless extraneous details such as that the workers can’t hear you because they’re listening to their iPods.)