The Trolley Problem

An interesting thought experiment that I vividly remember from undergrad philosophy courses is the trolley problem:

You see a runaway trolley moving toward five tied-up (or otherwise incapacitated) people lying on the main track. You are standing next to a lever that controls a switch. If you pull the lever, the trolley will be redirected onto a side track, and the five people on the main track will be saved. However, there is a single person lying on the side track. You have two options:

1. Do nothing and allow the trolley to kill the five people on the main track.
2. Pull the lever, diverting the trolley onto the side track where it will kill one person.

A variation of the problem that we were also presented with was:

You see a runaway trolley moving toward five tied-up (or otherwise incapacitated) people lying on the main track. You are standing on a bridge that runs across the trolley tracks. There is a large man on the bridge next to you, who if pushed over the bridge and onto the track, would safely stop the trolley, saving the five people but killing the large man. Do you:

1. Push the man over the bridge, saving the five people.
2. Allow the trolley to kill the five people

Which is the more ethical options? Or, more simply: What is the right thing to do?