There is no uncontroversial definition of free will. Some define it as the ability to have chosen otherwise, and some define it as self-determination. But I think everyone can agree on what a free choice isn’t. An un-free choice is when some external agency compels you to make a certain decision, whether you are aware of that compulsion or not.
An obvious example of an un-free choice is when someone compels you to do something by threats. Of course it isn’t completely un-free, but, like many things, free choice comes in degrees, in proportion to the extent the external agency influences the choice made. Given your psychology there may have been only one choice you could have rationally made, or only one choice you could have made that you wouldn’t have felt guilty about. And the external forces in question made you take that course of action instead of a number of others that were available to you. But there is still some freedom here, because there was still the possibility of doing otherwise (from your point of view), and so you did have some influence on your final actions, it was just that this influence was overshadowed by the pressures of the situation.
An example of an action that is even less free is the act of perception. When you look at the world you simply see things in a certain way, a way that is determined by what is out there an not be your preferences. Of course there are abnormal situations where we hallucinate, or simply close our eyes and imagine seeing things, but there aren’t examples of normal perception. Another example of an un-free situations is the science fiction scenarios where you are the victim of mind control, where thoughts are forced upon you that you would not have otherwise thought, pushing you down a course of action you would not have otherwise taken.
Free will then is when the majority of the factors that influence your choice are under your control, or in other words, when no external agency is compelling the decision (un-un-free will). So in normal situations do we have free will, defined as un-un-free will? Well normally our decisions are caused primarily by our brains. Certainly external factors (perception) have some affect on what happens in the brain, but the dominant cause, by far, of both decisions and future brain states is our current brain state. Thus whether we have free will or not depends on how our selves are related to our physical brains.
If we are materialists then we either identify the self with the brain directly, or with the functional properties of the brain. In either case since I am identical with my brain, and my brain is the primary cause of my actions then I am the primary cause of my actions, and thus my actions are free (because they are not un-free). On the other hand if we are epiphenomenalists, who think that the brain is a separate mental substance that runs in parallel to the physical brain, without the mind causally influencing the brain, then we would lack free will, since the brain would be an external agency that was in fact the primary cause of our actions, not us. Other possibilities, such as a separate mental substance that interferes with the workings of the physical brain are, of course, ruled out by modern science.
That covers the classical possibilities. But when I speak of the mind I am speaking of the combination of both conscious and unconscious mind. I assume that our self is identical to this sum. But what if we identified the self only with the conscious mind? Many of our actions would then become un-free, since the details of my breathing, my typing, ect are all caused primarily by my unconscious mind. Sure, the conscious mind seems to be the cause of some actions, but it seems possible that many of the thoughts that we have consciously, which are the cause of the actions that we think we are consciously in control of, are themselves created and put into the conscious mind by the unconscious. If this were true it would make the conscious mind controlled by the unconscious, and thus would make us un-free. But, first of all, the details of how the conscious mind and unconscious mind interact have yet to be fully spelled out, and secondly it simply makes more sense to identify the self with the sum of the conscious and unconscious mind. Our memories, our disposition, and our beliefs are usually unconscious, brought only into consciousness when the situation calls for them. Since it is natural to define the self in terms of memories, disposition, beliefs, and so on, and not simply by the contents of the current conscious experience, it seems natural to say that the unconscious as well as the conscious is who we are.
Thus, since materialism is by far the most plausible theory about the mind, I conclude that we are free.