A conception of 'free will' that is considered to be impossible if the universe is deterministic has a difficult question to answer: how does non-determinism enable it?
Suppose I'm making up my mind whether to buy some item. There is some last-nanosecond non-deterministic quantum event that causes a neuron to fire, that wouldn't otherwise have fired, and I buy the item. What was 'free' about my decision if that quantum event was not caused or influenced by 'me'?
Non-determinism informally says that some things in the universe may be unpredictable. If my decisions depend on unpredictable events in the universe, how are they 'free'? It sounds like 'at the mercy of random events in the universe'.
So it's not that the world can be deterministic and you can still have 'free will', it's rather that if the world was non-deterministic, you still couldn't have that sort of 'free will'.
Oh jeez, there's no happy way of looking at this is there.
Seriously though -- this is extremely depressing to me, it's literally giving me terrors right now. It's reducing all that I love and value to nothingness. How do you guys deal with this?
An important thing in what I wrote is that it only applies to certain sorts of free will. The sorts of free will it applies to include the idea of 'free will' that many scientifically educated (and usually philosophically untrained) people have. Let's call it the 'natural' or 'naive' idea of free will. In that view, free will and determinism are incompatible.
However, as others have pointed out in parallel answers, there are 'compatibilist' views in which free will and determinism are compatible. The sorts of 'free will' that those views apply are different from the naive idea of free will and the important point to take away from that is: it may not be clear to you or me what the phrase 'free will' actually means.
I do not subscribe to compatibilist views, because they define 'free will' as something that I do not believe is worth wanting. However, that begs the question: what is a definition of 'free will' that I do believe is worth wanting? And I have found that I cannot answer that question: I cannot define it satisfactorily in a way that is amenable to philosophical analysis, while all definitions that can be analyzed are unsatisfactory.
So it boils down to this: I believe it is important to have 'free will', but I cannot define what it means to have free will. As I cannot become unhappy about not having something that I do not understand clearly enough to reason further about, my life is effectively no different from never having thought about 'free will' at all.
So that's how I deal with it. In a way that is unsatisfactory to many people, because it seems to allow for a bit of 'insert magic here' just to satisfy my emotional need for the existence of some intuitive notion of free will. To which all I can say is: yes, I believe that believing "I don't understand" and being happy is better than believing "the best answer we can come up with is depressing" and not being happy.
I personally go with a computability/compatability argument. If 'you' are some sort of process analogous to a computer program, you can be totally deterministic yet unpredictable. You can't predict in advance the outcome of running some program, c.f. halting problem, without simply running the program slightly faster. Running the program slightly faster is identical to the initial process anyway, since it must get exactly the same inputs. Hence, you are a computational process experiencing itself, everything you feel is valid and no-one can take that away from you :)
Suppose I'm making up my mind whether to buy some item. There is some last-nanosecond non-deterministic quantum event that causes a neuron to fire, that wouldn't otherwise have fired, and I buy the item. What was 'free' about my decision if that quantum event was not caused or influenced by 'me'?
Non-determinism informally says that some things in the universe may be unpredictable. If my decisions depend on unpredictable events in the universe, how are they 'free'? It sounds like 'at the mercy of random events in the universe'.
So it's not that the world can be deterministic and you can still have 'free will', it's rather that if the world was non-deterministic, you still couldn't have that sort of 'free will'.