Lots of theological debates center around the religious idea of free will. Some varieties of theists, i.e. Calvinists, don't believe in free will at all. Some atheists (like my friend Denis Loubet) don't believe in free will either, believing that the notion is incompatible with a completely materialistic universe.
Those are all interesting topics, but one issue I find equally interesting is whether "God," as Christians define him, can have free will. I think I'm borrowing this line of reasoning from an old Raymond Smullyan book, although I can't remember exactly where.
God is supposed to be omniscient. He knows everything about the past, present, and future. In fact, his knowledge is so complete that he must know every action that he himself will take in the future.
Now, suppose you yourself were granted the power of omniscience -- not omnipotence or any of the other useful attributes, but you know everything. Suppose it comes time to make a fairly mundane decision, like what you will eat for breakfast. You can have scrambled eggs or oatmeal. So you wonder, what am I in the mood for? Scrambled eggs, or oatmeal? But this is an easy decision: you are omniscient! Simply use your unlimited knowledge to peer a few minutes into the future, and see what it is that you will have for breakfast. And when you look at your future self, you know, as a matter of absolute certainty, whether you will be eating eggs or oatmeal.
But wait a minute. What if you are in a perverse frame of mind and wish to exercise your free will? So you say to yourself "Okay, here's what I'll do. I'll check the future, but I won't do what it says. If I see myself eating oatmeal, then I'll pick scrambled eggs. If I see myself eating eggs, it'll be oatmeal."
Now what does that mean for your powers? If your vision is guaranteed to be accurate, then you don't have the free will to change your decision. But if you can change your decision, then your vision was wrong, and you are no longer omniscient.
This is one reason why I conclude that no being can be both omniscient and free.