Feeding wild animals is never a good idea for backpackers and campers; not only is the practice often unhealthy for the animals from a nutritive standpoint, but it tends to promote tense confrontations. Bears, catholic in their diet and enormously powerful, can become dangerous if they associate human beings with low-effort meals. Backpackers, who more than any other outdoor recreationists may be penetrating remote, heavily-used bear country, should never feed ursids --- and that means not only withholding scraps from begging animals but also keeping a clean camp and securing stored supplies.
Bears are rigorously omnivorous --- most species will munch on anything from pine nuts and grubs to big ungulates and carrion. Grizzly and black bears construct their active season --- most retreat to dens for the winter --- around the availability schedule of their favored foods, and are intelligent enough to quickly incorporate a new nutrition source to their wide-ranging rounds. Bears in heavily-used back-country, like parts of the Boundary Waters wilderness in Minnesota, will frequent summer campsites in the expectation of hand-outs or scavenged goods if careless campers have engendered such a tradition.
Bears that do associate campsites with easily acquired food are inevitably going to lose some of their ingrained fear of people. This happens with many species, from squirrels to coyotes --- but when it's a 400-pound-plus bruin with powerful jaws and swiping paws, it's a whole different proposition. According to leading ursine authority Stephen Herrero (author of Bear Attacks: Their Causes and Avoidance), many of the black and grizzly bears implicated in attacks on humans in North America are animals habituated to people because of hand-outs (less common than in the early- and mid-20th century) or scavenging food and garbage from sloppy camps and waste sites.
Avoiding A Dangerous Precedent
You may place yourself in danger by feeding bears directly or indirectly around your back-country campsite --- but you also threaten those backpackers coming after you, who may encounter such habituated animals. Be respectful of your fellow campers, your environment, and the bears themselves by properly preparing and storing food in the wilds: Try to cook and eat away from your sleeping area, keep a clean wilderness kitchen, and stash food supplies with rope on upper tree branches some distance from your tent.