So often graphite and charcoal go hand-in-hand. Done correctly, they complement each other. Done poorly, however, and an otherwise good drawing just won't look right. What are the differences, and how should you use each?
First take graphite. The traditional pencil, so easily obtained, yet often underrated. Graphite ranges from very hard and very light (9H) to very soft and very dark (9B). With this range of values you can produce great depth in your drawings. You can get very dark with a pencil, but it's not the same blackness as charcoal, and here's why: graphite is shiney. This makes it very good for some applications and very bad for others. For example, I like to do rocks and leaves in graphite. The whites or light irises of an eye are also good candidates for graphite.
Charcoal, on the other hand, is black and soft. You won't find the range hardnesses that graphite has, but you don't need it. Charcoal can give very dark black, or added to the paper with a stump or tortillon to give very light grays (see my Polarity drawing). Since it is so soft and blends so easily, it is the better tool for drawing fur, especially soft or fluffy fur like that of cats and koalas. I tried using a combination of charcoal and graphite for my latest tiger, and it just didn't come out right. I think if I had done it all in charcoal it would have come out better. But I was experimenting. On the other hand, I used graphite for my deer (almost finished), and I think it worked. Deer fur (hair?) is much coarser. I also prefer charcoal for backgrounds, especially even-toned areas. In fact, Hillberry says charcoal is best for background and graphite for foreground because of the difference in the way they reflect light.
While these are some good guidelines for which to use when, it ultimately comes down to your ability and comfort. Don't be afraid to experiment.