I have been given a request for a topic. Since that is an exciting occurrence that I don't want to discourage, I figure I should try to attend to the request (it has taken me a long time, but hopefully that won't count against me too greatly). The subject I am going to discuss, therefore, is free will. It is a topic that I am not a great fan of, but it is virtually impossible to study the brain and intelligence in any manner without having the question of free will pop up from time to time and leer at you. The reason I am not a fan of it is that I think it is a subject that has been marred over the centuries by association with a great deal of analysis that is not reality based. From Plato's conception of the soul in three parts to Descarte's conclusion that humans have souls and all other animals are simple automatons, there is a huge amount of crap unloaded by people who are largely unchallenged due to their eminent names. I don't actually have a name (hopefully it is appropriate to insert a yet here), nor have I taken any courses in philosophy of the mind or anything like that. I just thought it was appropriate to point that out.
Free will is one of those loaded subjects that everyone seems to have an opinion about. Most people seem to accept that we do have free will based on the fact that they feel like they have free will. However, without invoking a magical or paranormal exception for the mind (like a soul), it is difficult to reconcile the idea of free will with deterministic physical laws. Some people have tried to squirm their way around this by appealing to the craziness that is quantum mechanics, but those are usually fairly shaky and tenuous attempts. The fundamental problem is that people intuitively think in terms of whole entities - it is hard not to visualize functions of the brain as a tiny homunculus moving switches and making decisions. Of course, no such little fellow has been found, as well as that sort of visualization begs the question of how his brain works.
The way I tend to think of the subject of free will is in the context of a dynamical system. The brain as a network of little computational units is a physical entity and therefore must follow physical laws in the same way that everything else does, so in that way it is as deterministic as anything. However, it also an exceptionally complex system that feeds much of its own output back into itself (sometimes in round-about manners), making the analogy to an iterative mathematical function somewhat appropriate. Though most of the dynamics I have studied is based on simple functions (like the quadratic function), even those very simple functions can exhibit chaotic behaviour that is virtually impossible to predict. When systems become even more complex, you can have a deterministic system that still follows all physical laws, but requires a system at least as complicated as itself to predict the exact outcome. An example of such a system is the weather. We can make probabilistic claims about the future weather, but we cannot completely predict its behaviour (and beyond a week, most predictions about the weather are fairly useless other than the very general ones like "as it gets closer to winter, it is going to get colder"). Similarly, we can make probabilistic predictions about a person's behaviour (most people, when presented with a sudden loud noise, will jump and look about in a startled fashion). As we get to know a person better, we get better at our predictions (when my girlfriend and I are out for a walk and we see a person walking a dog, I can very closely predict the degree to which she will get excited about seeing the dog based on its breed and age (puppies have a clear advantage over older dogs)). Likewise, after living in an area for a while, most people get much better at predicting what the weather is going to be like. Exact prediction, however, is still impossible, especially as one moves farther into the future.
In Hobbes' Leviathan, he spends the opening chapters arguing that the thoughts of man are entirely dependent on his previous experiences. Humans cannot come up with anything entirely novel that is not some sort of derivative of earlier sensory perceptions. Even things like mythological creatures (like centaurs) are still a combination of known things (in this case, a man and a horse). While this is not entirely true (many neurons in your brain generate signals on their own, especially before birth and during infancy), it is quite close to the truth, in that our thoughts are linked to our environment and experiences. Some of those factors are beyond our control and also unpredictable (making the complexity of the system even greater).
Putting all of these points together, my basic conclusion about free will is that it is one of those things that largely depends upon definition, but for all practical purposes it does and ought to be treated like it exists. Saying that an absence of free will makes us deterministic automatons is an oversimplification, because determinism does not mean machine-like lack of behavioural options.