This question of free will only makes sense if you believe in god. If you're an atheist then the question just doesn't make sense.
UPDATE: A brief summary of compatibalism: http://www.rep.routledge.com/article/V014SECT1
According to them dogs do not have free will but people do. Probably talking about ethics and moral side of "free will" question, not physical or religious. But even there "free will" is just an illusion in your mind.
This is a philosophical question, and as such, can't really be answered experimentally. At the risk of sounding sophistical and clintonian, it depends on what you mean by "'really' free". You can be controlled by environmental factors and still exercise free will by some definitions of that term.
Just because God may know what you will do ahead of time, does not mean God caused you to do it.
Sure it does.
But feel free to disagree if you like. Or can.
Within the confines of science, and outside the consideration of religion, philosophy, or faith, free will simply refers to the limits of determinism. i.e., is it possible to have enough information about the initial state of someone's life to perfectly predict all of their actions? At the moment, quantum mechanics says no, and so science says we have free will.
However, it's not a black-and-white, on-or-off thing either. Psychology and sociology can both make predictions about a person's life based on specifics of the person's initial state, and as genetics and biological sciences continue to touch borders with psychology, we find more and more that there are physical forces which influence the way people behave.
So, to what extent is there free will? If someone is born with the genetic traits for schizophrenia -- pre-determined by their parents, and their parents before them, and so on -- then just how much free will does that person have?
The question of determinism has nothing necessarily to do with religion.