It all depends on how you define 'free will'.
Everything else that happens in the universe appears to be determined by cause and effect--the Copenhagen interpretation of quantum mechanics notwithstanding. (There are, in fact, other interpretations of quantum mechanics which are compatible with determinism, like the many-worlds intepretation) We live in a deterministic universe--at least, at the level at which we experience it, and at which we have evolved to cope with it.
So the question is: is free will compatible with determinism, or not?
If you say 'yes,' then you're a compatibilist. You believe that a person has free will so long as they are free to will what they would ordinarily will, given their particular combination of character and circumstance.
According to this interpretation, an ordinary person who is under duress, i.e. with a gun to their head, does not possess free will: it would take an extraordinary person to resist that kind of duress, and choose to take a bullet in the head; most people just do not possess that much strength of character.
So most people in our society are compatibilists, whether they know it or not. Our entire legal system is built on this philosophical position. A person with a gun to their head would not be held responsible for whatever crimes they were ordered to commit--at least, not fully responsible. We recognize that the fear of death has robbed such a person of their free will--that is to say, robbed them of their freedom to choose what they would ordinarily choose, and act as they would ordinarily act.
Certain people, however, reject this common-sense position, and try to argue that free will is not compatible with determinism. These people are, unsurprisingly, called 'incompatibilists.' They argue that free will is something more than just the freedom to do what we ordinarily do: this, they argue, is merely freedom of action, not freedom of will.
Most incompatibilists are so-called 'libertarians.' They argue that our choices are in no way determined: that our choices, unlike everything else in the universe, are somehow, magically, not subject to cause and effect.
To be fair, this position has a strong intuitive appeal: our choices do not seem determined, when we reflect upon them. And some very honest and respectable philosophers, like Thomas Reid, have held that our intuitions about our choices are true.
But people who believe in libertarian free will are faced with an impossible dilemma. Either our choices are determined, or they are not. If they are determined, then they are not 'free', by the incompatibilists' own definition. But if our choices are not determined, then they are also not 'free'. If our choices are not caused, then they're just random, unpredictable events.
This is important because most people who embrace libertarian free will do so because they fear that determinism undermines ethical responsibility: they believe that, if our choices are not completely free, and in no way determined, then we cannot be held responsible for them.
But what these people fail to realize is that, if our choices are completely free and undetermined, then we also cannot be held responsible for them. If our choices have no causes, then they're just random events--and no one can be praised or blamed for events that happen randomly.
Far from undermining moral responsibility, determinism is necessary to ensure moral responsibility. There is no point in punishing someone for their evil deeds, or rewarding them for their good deeds, unless those deeds are somehow determined by their moral character. Punishment and reward are justified because they change the characters and circumstances that determine people's choices.
What's more--and I think this is my own original contribution to the free will debate--it's impossible to prove that libertarian free will exists. To argue that libertarian free will exists is to argue that, if a person makes a choice, then that the exact same person, under those exact same circumstances, could have made a different choice. And there is just no way to test that hypothesis.
Given these problems, why do so many people still seem to believe that free will is incompatible with determinism?
I have come to believe that this fallacy has been promoted by Christian apologists as an alibi for their god, and a solution to the problem of evil.
If everything in the universe is determined, then God is responsible for everything that happens therein. That is to say: God is responsible for all the evil in the universe. He made it all happen, when he forged the first link in the chain of cause and effect.
This is unacceptable to Christian apologists, who want to believe that their God is all-good. So they promote the idea that human choices are undetermined as a way of blaming the victim, and getting their god off the hook.
Some people are so disgusted by this intellectually-dishonest, victim-blaming position that they embrace its reverse. Instead of identifying the source of the problem, and becoming compatibilists, they become ethical mechanists. They argue that, since the universe is deterministic, and free will is incompatible with determinism, then there simply is no free will, and nobody is responsible for anything.
I used to hold this opinion, in fact. But in time, I realized that it was just as wrong as its opposite, and that the heart of the problem lay in true and false definitions of free will.