Free will
Free will implies that our conscious mind is fully in control of our actions. At any point in time, we are free to decide exactly what we want to do, and we are fully responsible for the choices we make.
Incompatibility With the Materialistic View of Consciousness
The materialistic view of consciousness is incompatible with any notion of free will. Our consciousness is a reflection of the chemical interactions of our neurotransmitters. All of our decisions are deterministic, and if we could accurately model the universe on a quantum level we could predict what any of us will do at any point in time.
This notion does not sit right with a lot of people. Traditional religious morality relies on the assumption of free will to impart personal responsibility on the individual. They reason that without free will there can be no responsibility, which would lead to a society where nobody is accountable for any of their actions. This is, of course, poppycock.
Legal Implications
The fact that free will does not exist in reality does not need to take away from the legal responsibility for our actions. We certainly need to rethink our notions of justice when we know that we are all products of our environment. The threat of punishment has proven to be ineffective at deterring crime, since the threat is theoretical until after the crime has been committed and the perpetrator caught. Prevention is far more effective. Take away the conditions that lead to criminal behavior and people will reflexively avoid it, rather than being forced to choose between ethics and survival.
Free will doesn't exist, but our legal and ethical systems must still assume that it does.
However, our institutions should be built around the assumption that free will does not exist, so their efforts can be focused on guiding people towards best practices by creating an incentive environment that makes the best choice the easiest one.
Free Will and Quantum Mechanics
This is not an excuse to insert quantum woo into the conversation. However, the fact that to the best of our knowledge quantum mechanics operates on a probabilistic level rather than a deterministic one does mean that on the molecular level, the firing of individual neurons can only be predicted statistically. This means that we cannot know for certain what someone will do, only that they will choose the one option X% of the time and another option Y%.
A course on Behaviorism and an introduction to neural networks is the best way to get a basic understanding of the role that reinforcement and probability have on human behavior and decision making.
The fact that we don't always know which option we will choose helps maintain the illusion of free will, but it is not the same thing as being able to control the firing of neurons in our brains using our minds.
The Same Arguments But In a Popular Book
Check out Determined: A Science of Life without Free Will for an in-depth look at these arguments by a professional neuroscientist rather than an amateur philosopher. Or if you're tired of reading, here's a couple of podcast interviews with him (one short, one longer).
The materialist perspective on free will is nothing new, but Spalosky's book is one of the best analyses of the subject available and references the latest research.
One song about having freewill, and one about subverting it.