I've encountered a lot of bears, a few grizzly (brown) but mostly black. Never really felt in any danger. A good practice is to make lots of noise and not move too quickly, most bears would rather not meet you. And when you do see one try and keep a safe distance away.
Fishing from a bridge in Yakutat, Alaska there used to be a big bear who would sit on the river bank watching the bridge. Every now and then he'd come up and run the fishermen off to take your fish or bait, or any goodies you left him. I learned to put salmon into the truck when caught, keep lunch there, and grab any bait when running back to the truck. You could tell the tourists from the locals, most of the locals ignored the bear or yelled and threw rocks to run it off. To my knowledge it never actually hurt anyone. In Alaska I have felt more threatened by inexperienced folks carrying guns for bear protect than by bears...