This is caused by sharp, low poly geometry with smooth shading (you'll notice that the problem goes away with flat shading).

There a couple things you can try:

• Adding more geometry (works well for curved objects)

No subsurf:
Subsurf level 2:

• Using an edge split modifier (works better on objects with sharp edges)

Without edge split:
With edge split:

This is caused by sharp, low poly geometry with smooth shading (you'll notice that the problem goes away with flat shading). It's true that bounces can also cause dark spots (as mentioned in the other answers), but I think this is the issue in your case.

There a couple things you can try:

• Adding more geometry (works well for curved objects)

No subsurf:
Subsurf level 2:

• Using an edge split modifier (works better on objects with sharp edges)

Without edge split:
With edge split: