There are many differing opinions about what makes a suitable bear defense gun, but the truth is that so long as certain guidelines are adhered to, the actual caliber selection is not all that important. Bears, especially brown bears (referring to the species, both black bears and "grizzlies" can range in color from tan to dark black), have a nasty ability to absorb amazing amounts of lead with no apparent loss of power or mobility. There have been many cases of attacks in which a mortally wounded bear has continued to maul its victim(s), before crawling off to die itself, even when hit in the vitals with a "stopping" rifle caliber. The following are my opinions only on what makes a suitable bear defense gun, and should be treated as such.
From what I have observed, opinion seems to be fairly evenly divided between those favoring the use of a high-powered rifle and those advocating 12 gauge slugs, with the rifle faction holding a slight edge. With a shotgun, you will want a pump action with a fairly short barrel using foster-type slugs, extended magazine optional. Unless you are highly trained in their use, stay away from pistol grips; while they make carrying it much easier, in the unlikely event that you need the gun they could easily cause you to miss, and with a bear you will not get a second chance. If you choose to carry a rifle, a good reliable bolt action in the 7mm, 30-06 range on up should be adequate, the upper limit determined by the competence of the shooter. If you can handle the larger calibers then go ahead and use them, but with bears bullet placement is MUCH more important than incremental increases in power. Stick to the heavier bullets for a given caliber; you want all of the penetration you can get. For a pure bear defense weapon, stay away from scopes. Open sights are much faster, and within the close ranges at which bear defense takes place, they are more than adequate; whereas a scope in which you can see nothing but indistinguishable hair is useless. I would not choose a semi-automatic rifle or shotgun, besides being heavier to carry around, to me the possibility of a jam is unacceptable. My personal choice is an old, beat up Savage 110 in .30-06 with open sights, though I have often considered putting a shorter barrel on my 12 gauge and using it instead.
Pistols are a really bad idea for bear defense, in my opinion. While some pistols are certainly better than others, these are generally much more difficult to control than a rifle, while being much less effective. The only times when I would consider a pistol is if I were involved in some activity which made carrying a rifle not only impractical, but impossible. One example of this type of situation is my brother, who often fishes from a float tube or with chest waders in deep water. I avoid the problem by using a canoe. Out of the people I know who do carry pistols for bear protection virtually all of them have a rifle or shotgun of some kind nearby, and the pistol is only a backup weapon. A good minimum pistol caliber is .44 Magnum, though some are comfortable with a .357.