Newcomb's Paradox is a well-known problem, and I won't try to go through all the angles, interpretations and arguments. The basic problem is this (taken from Wolfram):
Given two boxes, B1 which contains $1000 and B2 which contains either nothing or a million dollars, you may pick either B2 or both. However, at some time before the choice is made, an omniscient Being has predicted what your decision will be and filled B2 with a million dollars if he expects you to take it, or with nothing if he expects you to take both.
It's common to suppose that the Predictor is not necessarily omniscient. It can just be an extremely reliable supercomputer, say. Grey's Labyrinth gives a nice introduction to the problem and a very clever go at a solution, too. The claim is that it is most rational to choose just one box. I agree. Here's why.
Our actions can be extremely sensitive to external conditions, so that it seems practically impossible for the Predictor to accurately predict what people will do ahead of time. We cannot imagine the level of knowledge the Predictor must have to accurately predict our behavior, and this is perhaps why most people just don't take the Predictor seriously enough--and that's why the option of taking both boxes is perhaps most attractive. It's hard to take the Predictor seriously, not because we intuitively believe we have contra-causal free will, but because our actions are so utterly unpredictable.