Stan,
Of the predators in the US, the most likely to attack humans are the grizzly and mountain lion. This said, they are very, very rare. When I last visited Yellowstone (a few years ago), they emphasized that bison injure more people. When I lived and hiked in the Big Sur region of California, I never saw a mountain lion (although my bud swears one ran in front of the truck one evening as I dozed on the way out). In New England, where I live, moose are among the more dangerous animals in terms of injuries. More broadly, animal attacks all totaled are much less common that more mundane backcountry threats like hypothermia, getting lost, falling, and heart attacks. And of course, the most likely way to get killed or injured from a backcountry trip is during the drive to and from the trailhead. Strongly suggest reading a good general backcountry book like Colin Fletcher's "The Complete Walker", creating your own version of the "10 essentials" (my list is here and it includes a knife: http://home.comcast.net/~pinnah/DirtbagPinner/essentials-list.txt) and driving safely.
Regarding knives... I prefer to carry a knife with a blade in the 3" to 4" range. I like flat ground blades as they work wood well, which is handy when making fires. I also like a knife I can carry on my person even when I'm wearing a pack. For me, this means a folding knife.
Of all the animals discussed above, the only one that would make me change my knife selection (I carry an Opinel) would be the mountain lion. It appears to be the only animal for which it is suggested that you actively fight back. If I were hiking solo in known mountain lion terrain (I have in the past), I would be thinking about the same things from a knife that fighters think about; namely the ability to deploy it quickly under duress and the ability to stab. For a fixed blade, I would want a finger guard. I would also think about a "dangler" style sheath that could be used with a pack hip belt so that I always have it with me. For a folder, I would want 1 hand opening or assisted opening. Of these two styles, I would go with a tactical style folder.
I must emphasize that with all wild animals, knowledge is much more important than a knife. If you regularly hike in mountain lion terrain, you should read everything you can get your hands on about them and learn how to hike in a way that minimizes the chances of being attacked. Solo running is probably a bad idea.
Black bears warrant a fight. And if a .357 magnum is not available, the largest knife possible works.