I think there are three primary reasons philosophers are interested in questions about free will, at least they are the ones that motivate me to spend most of my time on them.
1. Free will is often used (by philosophers and non-philosophers) to pick out the sort of control over decisions and actions that agents need in order to be morally responsible for what they do--that is, to deserve praise for the good things they do and blame, and certain kinds of punishment, for the bad things they do. If we lack free will--defined in this way--then we would not really deserve praise and blame, reward and punishment, and perhaps even gratitude, indignation, and forgiveness. Figuring out how to define 'free will' as relevant to these questions is one of the most significant debates in the current discussions. And figuring out whether we have such free will, in the face of the possibility of determinism or physicalism or certain scientific discoveries, is another.
2. Furthermore, some people think (and some evidence suggests) that our beliefs about free will influence some of our other beliefs and behaviors. For instance, if we came to think we lacked free will, maybe we would be less retributive in our punishment and more forgiving of our friends and family when they screw us over, but maybe we would be less likely to control some of our bad impulses and we would screw each other over more. Some people also think that aour lives and relationships would lack certain kinds of meaning or importance if we lacked free will. Others think that lacking free will--understood as a kind of ultimate self-creation which is clearly impossible--is not very important for most of what we care about, including our relationships and the meaning of our lives.
3. We experience ourselves as having a certain type of control over our actions, including being able to imagine various options for future action and selecting among them. We might call these experiences of free will. It seems important to know whether such experiences are illusory, as some argue, or whether they are accurate in the sense that we actually have the sort of control and decision-making abilities that our experiences seem to represent. If nothing else, it's good to know the truth about things, so it'd be good to know the truth about how our agency works.
If readers want to think more about this stuff, they might go to Flickers of Freedom, a blog on these topics, including a recent discussion about point 1 above: http://philosophycommons.typepad.com/flickers_of_freedom/