This is an aspect of this debate that utterly fascinates me. Many people reading this have probably heard the argument that free will does not exist because the human brain is just a molecular computer. If we could measure it's state perfectly at a given moment, have knowledge of future inputs, and possess adequate classical computational power, we could perfectly predict the future decisions made by your brain. Hence, you are a deterministic creature with no free will.
Quantum processes underlie all classical processes, not unlike how the physics of individual water molecules underlie the behaviour of a river. While individual molecules or even drops of water can do bizarre things, the course of a river is easy to predict. A coin toss or weather patterns may seem random, but they're classical systems that would be utterly predictable if we had a perfect measurement of their current state, knowledge of input from outside the system in question, and the computational resources to work out their future evolution. As with a river, the weather, or a coin toss, quantum weirdness should average out on the scale of a human brain, leaving only classical predictability behind.
Or does it?
One aspect of this quantum weirdness I'm referring to is truly random behaviour. Single quanta (e.g. photons or atoms) can be manipulated to produce measurements with truly random results that are, according to quantum theory and every experiment conducted to date, impossible to predict, even with perfect knowledge of the system, knowledge of all inputs, and infinite computational resources. Free will and being unpredictable are intrinsically linked. If your brain is just a classical machine behaving according to the laws of chemistry and physics, you are predictable and have no free will. If your brain amplifies the results of quantum outcomes to a macroscopic level, your brain may be inherently unpredictable and thus you may possess free will.
Fascinating stuff!