John Frame (The Doctrine of God, pp. 138-145) gives a powerful critique of what is commonly thought of as "free will" (more specifically, libertarian free will, the idea that the will is not determined by anything outside of itself). Here are short excerpts from his points, with my emphasis added at the end.
1. The biblical data...about God's sovereign control over human decisions, even human sins, are incompatible with libertarianism. Scripture makes clear that our choices are governed by God's eternal plan, even though we are fully responsible for them.
2. Scripture does not explicitly teach the existence of libertarian freedom. There is no passage that can be construed to mean that the human will is independent of God's plan and of the rest of the human personality.
3. Scripture never grounds human responsibility (in the sense of accountability) in libertarian freedom, or, for that matter, in any other kind of freedom. We are responsible because God made us, owns us, and has a right to evaluate our conduct.
4. Nor does Scripture indicate that God places any positive value on libertarian freedom (even granting that it exists).
5. Indeed, on the contrary, Scripture teaches that in heaven, the consummate state of human existence, we will not be free to sin. So the highest state of human existence will be a state without libertarian freedom.
6. Scripture never judges anyone's conduct by reference to his libertarian freedom.
7. Indeed, Scripture condemns some people for acts that clearly were not free in a libertarian sense...such as Judas' betrayal of Jesus.
8. In civil courts, libertarian freedom is never assumed to be a condition of moral responsibility.... Libertarianism would make it impossible to prove the guilt of anybody at all.
9. Indeed, civil courts normally assume the opposite of libertarianism, namely, that the conduct of criminals arise from motives....We see, then, that rather than being the foundation of moral responsibility, libertarianism destroys it.
10. Scripture contradicts the proposition that only uncaused decisions are morally responsible.
11. Scripture denies that we have the independence demanded by libertarian theory. We are not independent of God, for he controls free human actions. Nor can we choose to act independently of our own character and desire. According to Matthew 7:15-20 and Luke 6:43-45, the good tree brings forth good fruit,and the evil tree brings forth evil fruit. If one's heart is right, his actions will be right; otherwise, they will be wrong.
12. Libertarianism, therefore, violates the biblical teaching concerning the unity of human personality in the heart....This integrity of human personality is not possible in a libertarian construction, for on that view the will must always be independent of the heart and all of our other faculties.
13. If libertarian freedom were necessary for moral responsibility, then God would not be morally responsible for his actions, since he does not have the freedom to act against his holy character.
14. Libertarianism is essentially a highly abstract generalization of the principle that inability limits responsibility.
15. Libertarianism is inconsistent, not only with God's foreordination of all things, but also with his knowledge of future events.
16. Libertarians...tend to make their view of free will a nonnegotiable, central truth, with which all other theological statements must be made consistent. Libertarian freedom thus takes on a kind of paradigmatic or presuppositional status. But, as we have seen, libertarianism is unscriptural. It would be bad enough merely to assert libertarianism contrary to the Bible. But making it a central truth or governing perspective is very dangerous indeed.
17. Philosophical defenses of libertarianism often appeal to intuition as the basis for believing in free will....But...an appeal to intuition can never the basis for a universal negative....Intuition never reveals to us whether or not we are determined by causes outside ourselves.
18. If libertarianism is true, then God has somehow limited his sovereignty so that he does not bring all things to pass. But Scripture contains no hint that God has limited his sovereignty in any degree. God is the Lord, from Genesis 1 to Revelation 22. He is always completely sovereign. He does whatever pleases him (Ps. 115:3). He works everything out according to the counsel of his will (Eph. 1:11). Furthermore, God's very nature is to be sovereign. Sovereignty is his name, the very meaning of the name Yahweh, in terms of both control and authority. If God limited his sovereignty, he would become something less than Lord of all, something less than God. And if God became something less than God, he would destroy himself. He would no longer exist. We can see that the consequences of libertarianism are serious indeed.