There's another version of the trolley problem that's even squickier than the "push a man onto the track" version...

“A brilliant transplant surgeon has five patients, each in need of a different organ, each of whom will die without that organ. Unfortunately, there are no organs available to perform any of these five transplant operations. A healthy young traveler, just passing through the city the doctor works in, comes in for a routine checkup. In the course of doing the checkup, the doctor discovers that his organs are compatible with all five of his dying patients. Suppose further that if the young man were to disappear, no one would suspect the doctor.”

-- Judith Jarvis Thomson, The Trolley Problem, 94 Yale Law Journal 1395-1415 (1985)

For some reason, it's a lot less comfortable to endorse murdering the patient than it is to endorse pushing the fat man onto the track...