I lived in Alaska for awhile. Grizzly bears are something to be afraid of -- many of the above posters may have had encounters with black bears, but grizzlies are a different story. Black bears rarely attack people, and even if they do it's normally a bluff charge. The best advice with black bears is to stand your ground, look big, and fight back if attacked.
With a grizzly, play dead, curl up, and cover your neck with your hands if attacked.
I did quite a bit of running up there, and my advice would be to yell "hey bear!" periodically and alter the pitch of your voice. This prevents you from surprising/stumbling upon a grizzly, and the pitch change spooks them (it's a sign of intelligence in nature). Also, run along roads with wide shoulders so you can see for a distance. This will prevent stumbling upon bears. There are a lot of cool trails up there, but there is too much potential for coming around a corner and surprising a grizzly. I came within 50 ft. of one once, and it's not something I ever want to do again. Roads are your best bet.