Whenever i see this question, to give it perspective i quote from the experience of the three rangers that went in to recover the remains of Timothy Treadwell and his girlfriend.(from Katmai)
"Ranger Ellis was standing with ranger Gilliland and Willy Fulton to his left. Ranger Dalrymple was slightly ahead of Gilliland when Gilliland suddenly yells, Bear! while pointing to the right. Ranger Ellis states that he turned and "saw an adult bear moving toward the group about 20 feet away". All four begin yelling in hopes that the bear would see them and move away. Ranger Ellis then states that he "perceived that the bear was well aware of their presence and was stalking them". Ranger Ellis, armed with a 40 cal. handgun begins to fire at about the same time rangers Gilliland and Dalrymple, who were each armed with 12 gauge shotguns loaded with slugs also begin to shoot at the bear.
Ranger Ellis fires 11 times while rangers Gilliland and Dalrymple each fire 5 times, dropping the bear 12 feet away. "That was cutting it thin" stated Ellis. After about 10 seconds the bear dies and Willy Fulton then reportedly says "I want to look that bear in the eyes" and states that he is sure that this was the bear that chased him back to his plane earlier. (Ellis 2003, pg 3)"
Others that have had more experience can respond to the caliber question, but whatever it is it better be big enough with excellent shot placement. As i recall they estimated the weight of the bear mentioned above at about 1000 lbs. the above info is found at
http://www.yellowstone-bearman.com/Tim_Treadwell.html.