What is the will?
It is generally the ability of the human mind to be able to choose or initiate action. It is voluntary, in opposition to fate or coercion. For someone, walking off a cliff may have been a choice (will), but the fall that occurred was not; that was gravity.
Free will assumes certain conditions. There must be a mind associated with it. Blind choices are not "free will". There must be a reason, a motive. Random choices are not "free will". There must be culpability. A person who makes choices by means of a free will is responsible for those choices; a person who makes choices because they were coerced is not.
Note, then, that the will is not a "power source", so to speak. That is, it isn't generating itself; it is the product of something else. And we know this to be true. For example, you cannot simply will to fly without some apparatus to fly because you lack the inherent ability and no amount of willing makes it so. Instead, your choices are determined by your desires, your preferences, your values, your appetites. Put simply, choosing what you don't desire, prefer, or want would clearly not be classified as "free will". Thus, free will is driven by what the Bible refers to as "the heart" or "the mind" or "the inner man" (Eph 3:16). Jesus said, "From within, out of the heart of man, come evil thoughts, sexual immorality, theft, murder, adultery ..." (Mark 7:21). Solomon wrote, "As a man thinks in his heart, so is he" (Prov 23:7). The will, then, is driven by the heart or mind of its owner.
Do we have free will?
Lately there has been a rise among materialist atheists that demand that humans actually do not possess free will. Since everything in their worldview is rooted in the material world, any choices made are the product of DNA, chemistry, hormones, whatever physical agents are acting on the person at the time. Thus, to them, free will is an illusion. On the other side, there is an entirely different set of people that argue that humans make no real choices at all. It is all fate. Everything is not simply determined, but hard-coded. You make no free choices.
In between these two are the two "softer" views. One is the "Libertarian Free Will". The other is "soft determinism". And, of course, there are gradations between these two. Libertarian Free Will declares the ability for a human being to make selections without any determination of the nature of the person or any divine agent. They argue further that if there is any determination of choices based on human nature or divine determination, it is not free will. Loosened slightly from this absolute (and illogical) freedom is the more reasonable concept of free will that assures us that humans can choose whatever they want. Pelagius suggested that this would include the ability of the will to reject evil and to seek and to serve God. You could choose to be moral enough to make it to heaven. Pelagius argued for Libertarian Free Will and was condemned as an heretic. Soft determinism suggests that humans make uncoerced choices, but always within the confines that God allows.
So apart from some atheist views on one end and some fatalist views on the other, most believe we have "free will", at least in some sense.
How free is it?
Ah, now, here's the rub. Are you going to answer based on how you would like it to be or how you think it should be, or are you going to answer as God says it is? Important first question. You see, the Bible isn't unclear.
I've already offered (yesterday) several examples of times in the Bible in which God intervened in human will. And still does (Phil 2:13). While this doesn't eliminate free will, it certainly requires that the will is not perfectly free. Solomon wrote, "The heart of man plans his way, but the LORD establishes his steps." (Prov 16:9). This is in keeping with the overall biblical claim that "Our God is in the heavens; He does all that He pleases." (Psa 115:3).
In other texts we read of the inability of Man. For instance, "The mind that is set on the flesh is hostile to God, for it does not submit to God's law; indeed, it cannot. Those who are in the flesh cannot please God." (Rom 8:7-8). That's "cannot". That is an inability. In John 12 we read that the Pharisees "could not believe" (John 12:39). Inability. Paul wrote, "Natural Man does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned." (1 Cor 2:14). "Not able." Inability. We cannot choose to do that which we are unable to do.
The will is free, but only so far as it is ... willing. To violate what you want is not "free will". And what the Bible says the unregenerate person wants is not obedience, repentance, agreement with God, etc. We always choose according to our strongest inclinations ("free will"), and God says, "The inclination of man's heart is evil from his youth." (Gen 8:21). How free, then, is your will?
I need to mention, here, what "cannot" means. Using biblical examples, there are various versions of "cannot". For instance, "Isaac was old and his eyes were dim so that he could not see." (Gen 27:1). This is a physical inability. He could not see. But a few chapters later we read, "When his brothers saw that their father loved him more than all his brothers, they hated him and could not speak peacefully to him." (Gen 37:4). This is a different "cannot". Isaac lacked the physical ability to see; these brothers of Joseph did not lack the physical ability to speak peacefully to him. They lacked ... the inclination. Without the inclination, they lacked the ability. In Genesis 41:49 it says that Joseph stopped measuring the stored grain because "it could not be measured." He lacked the physical capability of measuring all the grain. On the other hand, just a couple chapters later we read "They served him (Joseph) by himself, and them (his brothers) by themselves, and the Egyptians who ate with him by themselves, because the Egyptians could not eat with the Hebrews, for that is an abomination to the Egyptians. (Gen 43:32). "Could not eat with Hebrews." Clearly this isn't a lack of physical capability. Their mouths still opened, their teeth still chewed, their throats still swallowed ... they had the ability to eat with Hebrews. They did not have the inclination and, as such, lacked the ability ("could not").
In conclusion, then, I think it is abundantly clear that humans have free will. But unless we are careful with that, we can follow that "free will" term down a false trail. The Bible clearly indicates that God intervenes at times in human choices, and this demonstrates less than a totally free will. The Bible clearly indicates that God works all things after the counsel of His will, and this demonstrates less than a totally free will. The Bible plainly states that there are things we cannot do, either by physical inability or by a counter inclination, and this demonstrates less than a totally free will. Thus, Luther's claim that our will is in bondage is in agreement with Scripture in that we are bound by our nature and the nature of sinful man is sinful, and Edward's claim that our wills are free is in agreement with Scripture in that we are free to choose, but only in accordance with our nature. Can we choose? Biblically, yes. But don't understand that to mean that we are totally autonomous, completely without limitations. It is not, in fact, a contradiction to call a limited free will "free will". It is a contradiction to claim an unlimited free will in light of both Scripture and logic.
 Note that the text goes on to indicate who is "in the flesh" and who is "in the Spirit". "You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you." (Rom 8:9). Natural Man, then, before the indwelling of the Spirit, is in the category of "the mind that is set on the flesh".