This is an issue that I've had to deal with. My particular problem is that I want definition of the fur, but I still want the fur to look black. But when I illuminated my feline friend she turned brown. This is the problem with black cats.. They're often secretly very dark brown.
As pretty much everyone has said, the real issue is experimenting with the exposure to get enough light that you can see detail in the black fur, but not blow out the rest of the scene. I tend to dislike strong direct light, not so much because of the shadows but because it causes bright reflections off of the fur and it can actually add too strong a white component. I suspect my best option is to use one of those ultra bright halogen lamps that you reflect off the ceiling, that should soften the light some, and they tend to be dimmable so I can see if I can find the right brightness level that gives me fur definition without white highlights or turning her brown. I've gotten useful results bouncing a flash off the ceiling, but that's been kind of crude.. I think I just turned it on full manual power and manually adjusted the exposure to try to get a good result.
I think my best results to date came from an accidental lighting setup, she was sitting near the sun without quite being in the sunbeam, and on the other side of her a bright, shiny red sleeping bag was draped over a chair. The sleeping bag reflected red light against the direction she was facing, while her back was more strongly illuminated from the sun. Okay, so it's not ideal.. but I was pleased, it's still among the best shots I've gotten of her yet. The red gave her fur a nice rich tone, and the truth is she does show a slight reddish component to her coloration under strong light. She's not prone to being in locations with good lighting, either she hides in the dark or sits in direct sun, or worse still half in and half out of the sun.
I suspect some knowledge of studio lighting techniques would be helpful here. But I've always been a firm believer in ambient light shooting, so it hasn't been an easy change to start adding my own illumination.
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