Sam Harris has written a book attacking the concept of free will, and in so doing has already received wince-inducing slams from philosophers, notable among them Patricia Churchland's. Stung from this, Harris sought out another philosophical foe (although another of the Four Horsemen), one of the most famous living philosophers, Daniel Dennett. Where Churchland's comments only implied that she didn't think Harris's arguments were worth an extended response, Dennett's directly states as much. It's a fun read.
(By the way: reading this frankly brutal takedown of Harris by another of the Four Horsemen, it's hard to imagine another intellectual movement which openly and honestly exhibits its intellectual differences like this, and a lot of credit is due. That said, I hardly think this is about to cause a rift among the ardent philosophical naturalists of the world, which may say something about how important this discussion actually is.)
I'm not going to summarize the points made between Dennett and Harris, but rather point out some heuristic meta-arguments that might be informative. A fair question to begin any discussion of free will is: how will the answer affect our actions either way? Suppose that tomorrow, an air-tight incompatibilist argument emerges saying no, there is no such thing as free will, and even Dan Dennett throws up his hands: what will happen differently? How could this affect our decisions? After all, it was already all going to happen that way anyway, right? And we go about our business, as we were already going to. OR, a compatibilist argument emerges that says yes, we have free will, and here is proof of this concept - what would Sam Harris do differently after this revelation? So is this the 2014 version of trying to calculate how many angels can fit on the head of a pin? That is, are we debating a problem that only seems to exist because of other (bad) assumptions we're making? Some incompatibilists would likely say yes, that free will is a concept (like theism) that people think is coherent only because of the historical inertia of other assumptions or values we desperately want to preserve. This is all to say: if it's not clear how an answer to this question could ever affect anyone's decisions, then it's possible the concept itself is meaningless in the first place. (Never mind the practical value, which is not in question. It must certainly be zero.)
Nonetheless, it remains an interesting problem (I suspect because it's foundering on submerged bad assumptions), like the nature of consciousness, which is why I'm writing this blog post and you're reading it. So first, briefly, here are three points that no-free-will incompatibilists should better address or answer.
1. Our current understanding of morality and individual responsibility is destroyed by the removal of free will. As Dennett points out, this is not an argument for free will; if there's no free will, then we lose morality, and too bad for us. But to say that no-free-will incompatibilists like Harris do not give this point enough time given its importance would be too kind.
2. If there is no free will, then all of causality is an illusion as well. Why? Because every event has in some sense "already happened" (was set in motion at the Big Bang), or it's unknowable noise. That is to say, we're watching a movie, and what happens at 1 hour 12 minutes in was determined when the film was recorded, and it's not going to change, and the image of the man kicking the soccer ball doesn't cause the image of the soccer ball to move any more than anything else on the film. As with the observation about morality above, this also does not make an argument against no-free-will incompatibilism. But the problem with causality does follow directly from this position, and it's ignored by said incompatibilists, and has profound implications for epistemology and the scientific method.
3. If there is no free will, how can there be a "now"? If everything is caused and determined, then we're in a frozen block of space-time or a movie. A subjective sense of free will is certainly not an argument for free will. But it is very difficult to understand how there could be a sense of a present moment if there is no such thing as the present moment - that is, of a changing point in time that is asymmetric and special because it seems to be influencing other points in time, that cannot in turn influence it.
4. Libet's button-pushing experiment disproves only one fragile model of free will (though Dennett doesn't bring it up in his review). An easy solution, though one that would support a free will that most of us would not like, is epiphenomenalism, where the decision is being made by an entity with free will whose process our conscious selves do not have access to. Certainly if free will exists in any entity on Earth, it's humans, and humans are having this argument - but even proving that humans have not a shred of free will is different than proving that the universe we're in does not allow it.