I remember reading about this problem in noted theoretical physicist Richard Feynman's book "Surely You're Joking, Mr. Feynman!", but I don't think he included the answer! Instead of going to the library to check, I thought I'd ask everyone here.
Consider a hollow tube with two smooth right-angled bends in it, shaped roughly like a squared off "S" like this:
This tube is connected to a hose which attaches right in the middle of the tube, and the tube if free to rotate about its centre. The tube is submerged in a tank of water, and the hose is turned on. The water shooting out of both ends of the tube will push back on the tube making it rotate opposite to the direction of the water (i.e. if you are looking down at the tube and water is shooting out to the top-right and bottom-left, the tube will rotate counterclockwise).
The question Mr. Feynman tried to answer (with spectacularly funny results, but no answer) was: what happens if you run it in reverse, and start sucking water into the tube instead?