This is a fun little icebreaker.
You are presented with a choice of two distasteful situations. You pick which one you think is worse--maybe explain why you chose the way you did. Then, once you answer, you pose two choices for the next person to answer, and so on.
It's fun if it's Star Trek related, but it doesn't always have to be.
I'll start:
What's worse: Being served gagh for dinner, or finding a scabby bandaid in your plomeek broth?