There is no simple answer to this question. Unlike grizzlies and polar bears, which are fairly consistent, the dangerousness of black bears varies greatly depending on geographical location. It also depends on the individual bear. Even in the worst location (northern inland British Columbia), the great majority of black bears are basically shy and gentle beings. But in some places, you run the risk of running across the most deadly and utterly ferocious land mammal in North America, the predacious black bear. This fortunately rare creature is fully as terrible as the man-eating tiger of Asia. The worst examples are as deadly as a white shark in a feeding frenzy.
First, let us examine areas where black bears are NOT dangerous to human life. The most outstanding such area are the states on the Eastern Seaboard of the United States. There has not been a fatality due to a black bear in this area in more than a century. Most areas have not reported a serious attack in modern times, despite close contact between large bear and human populations. The bears show a tolerance and restraint that is truly amazing, despite often severe and foolish harrassment from pesty humans. Two examples from Great Smoky Mountains National Park will indicate this. In one, an older female was being followed and poked and prodded by a couple of little boys. She suddenly turned and nipped one of the boys 3 times. The 2 kids were terrified and ran away crying. When the bitten kid was examined, there were no marks of any kind on his skin. In a similar case, a small child who was pestering a big male was grabbed by the neck and held firmly against the ground by his powerful jaws. Again, upon examination, the upset and terrified child showed no signs of injury.
"Bear attacks" from this area overwhelmingly involve trivial injuries. They are almost always the result of exasperated black bears "disciplining" humans who bother them as if they were naughty cubs. The incidents clearly demonstrate that the bear had no intention of actually harming the person. The few exceptions where significant injury occurs involve wounding a bear or cornering it, or threatening or actually harming a female's cubs. Eastern mama bears put on a very impressive threat display, but they rarely actually attack unless severely provoked. Bear researchers have calmly handled screaming cubs while mama bear huffed and puffed worriedly in the background.