So as to contribute more than just a plastering of links you could have found on the bottom of the page, I'll add my own response. I am a bit of a compatibilist. I don't particular like categorizing myself with these philosophical labels. I'm not joining some party for a particular ideology regarding free will.
What I believe is the most important ideas of free-will is those concerning agency and the agent itself.
Scientists have developed models of agents that behave according to particular patterns in complex adaptive systems. These agents, from the modelers perspective, are doing exactly what is expected. Randomness may have been programmed into the agents' behaviors, but does that mean that their behaviors are no longer determined?
Moreover, the agents interacting within the system may create higher level behavior that is unexpected or unpredictable.
What does it mean to be "determined", without predictability? What does it mean if even if somehow we could start the process back to the same exact "initial conditions" the behavior is still unpredictable?
From the perspective of the agent, it will get certain inputs (including perhaps some random ones and ones "internally" generated). It then "chooses" a behavior in response to those inputs. From the agent's perspective, does it matter that it's framework for making a choice was one that was already programmed into it?
If we step back, and look at ourselves as agents in this massively complex system, with our own past histories, genetic programming, psychological conditioning, and basic capabilities. Even if we are acting only according to our "programming" (perhaps with some randomness thrown in), are we acting on our will? or are we merely doing what is in our nature at the moment (even if nature largely based on past nurturing)?
For us at least, we have the perception of choice, and what does it mean to "choose" outside of that perception anyways? "Will" seems like one of those things that is inherently subjective. Talking about it's "existence" outside of the subjective context of the agent doing the choosing seems nonsensical to me. But, I may be missing something fundamental.
Accept the past. Live for the present. Look forward to the future. Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of  data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
I find the existence of free will implausible. My reasons are as follows:
Mind-body dualism, that is, the belief that mind is something separate from the body, seems implausible in the light of this. The man had a brain injury, and his entire personality changed.
Given this, what mechanism could one expect to find in nature that would explain free will? I suppose at this point people like to invoke quantum mechanics, but I don't understand quantum mechanics and I don't know if the people doing that do, either.
Free-will is every bit as unfalsifiable as a belief in God. Nobody can prove free will doesn't exist through empirical means that can be replicated, so it should go out the window, if God goes out the window because of such a standard.
Moreover, personal experience and analysis, while not perhaps verifiable, suggests that people always make their choices based on past inputs, whether they are aware of it or not. There is no randomness to it. There is a certain level of predictability, although I should qualify this by saying that much of the time, when we interact with each other, we are interacting on the basis of incomplete information. Because the information is incomplete, the choices appear more nebulous and somewhat "random."
I'm with you on that. Free-will is a theoretical concept and unfalsifiable. We can prove definitively that some degree of determinism is at work in human choice and it is also possible that we are entirely deterministic.
Considering the possibility that we are entirely deterministic, merely observing the cause-and-effect processes of our lives and genetics, increases my compassion for everyone. Even the evil tyrant can draw a degree of cautioned sympathy if you see him/her as a Being observing the process of being a tyrant. It makes it easier to forgive others.
As someone who overanalyzes everything, I've also been amazed to see how many of my own inexplicable choices (and the splicable ones) can be traced to my formative years. It's kinda spooky when you start to look deeply enough into your own psyche and see all the patterns align.
I hope for free-will, but I interact with others based on the greater possibility of determinism driving their choices and behavior. Sometimes I'll even encourage myself or others with the theory of free-will because perhaps it introduces an element into the deterministic system that makes it easier to make a choice outside of previous determined possibilities. It means introducing the idea of a choice going against nature and environment into a system where aligning choices with genetics and environment will only get you a bad result.
The first man to raise a fist is the man who's run out of ideas. H.G. WELLS
The first principle is that you must not fool yourself, and you are the easiest person to fool. FEYNMAN If this is monkey pee, you're on your own.SCULLY
Should you go for Chinese or pizza? Throw a coin and let it decide. Who made that choice? Was that freewill? Are you the coin or are you a person controlled by one? Are you the unpredictable winds blowing around coin and shaping it's fall? It's the same problem with quantum mechanics, the same with a soul. Freewill is fundamentally about the displacement of the self, like a more personal version of god of the gaps. But all these thoughts experiments, and the way we've rationalized free will throughout the years, kind of tell you something. We try to make sense of freewill by empowering something to govern us in a way we can't predict or know how it works.
The essential experience we are trying to rationalize with freewill is not knowing why we do something. It's what we experience before the coin falls to the ground and we've seen which way is up, the experience between the time a new question or situation comes up and the moment when we've made a choice and know the answer. We are self aware, but not enough to never be surprised. Later you will add this to the list of things you've done, later it will fit in the patterns you know yourself by or maybe even teach you new patterns, but right now you are making a choice and you aren't sure what it is yet. And that experience is real. Maybe every particle in your brain had no where to go but the place it ended up in, but it didn't get there until it did. You really are processing an experience between multiple perceived possibilities, you are taking a cognitive action of making a choice.
Your will isn't free, but it's your own, and it's choices are real.
I voted Jar jar binks. Because George Lucas had a choice. You didn't have to do it George! You didn't have to do it!