Many people's goals on this web-site are sufficiently grandiose to make utilitarianism unsettling. How repugnant a thing would you be willing to do to increase by a small but measurable amount the probability of human civilization birthing an astronomical utopia? It would be easy to write a post with lots of variations on this but I think it would be in bad taste (not a utilitarian reason not to do it, though).
A few ideas have been given elsewhere:
'No, it is real. The Brotherhood, we call it. You will never learn much more about the Brotherhood than that it exists and that you belong to it. I will come back to that presently.' He looked at his wrist-watch. 'It is unwise even for members of the Inner Party to turn off the telescreen for more than half an hour. You ought not to have come here together, and you will have to leave separately. You, comrade'--he bowed his head to Julia--'will leave first. We have about twenty minutes at our disposal. You will understa...
Joshua Greene manages to squeeze his ideas about 'point and shoot morality vs. manual mode morality' into just 10 minutes. For those unfamiliar, his work is a neuroscientific approach to recommending that we shut up and multiply.
Greene's 10-minute video lecture.