It's interesting this bear/wolf/mountain lion concern - and attacks happen often enough that it's worth being concerned.
That said, I've hiked, backpacked and traveled the wilderness for most of my fifty-odd years with very few problems with predatory animals. One time in Alaska a smallish black bear tore into our cooking area in the night and made quite a racket banging things around, looking for food. We scared him off easily enough, we were fishing and backpacking, not hunting.
Took these photos a few weeks ago on another fishing trip to Alaska. The presence of big bears does get my attention:
I don't recall seeing a wolf in the wild, although the possibility of that happening has become far stronger in the past ten years. I've heard them though. Quite a sound when backpacking alone or in a small group. Have come across a few cougars over the years - feel very lucky to have seen several of them in the wild. They never bothered me any, although after seeing one I do find myself looking around a little more, and over my shoulder quite a bit! Bears seem by far the most likely big predator to come into camp.
Some fine advice already posted above. Here's a few of my thoughts:
Travel in a group. I often violate this one - preferring sometimes to hike, ski, camp, fish and hunt alone - but am sure it's safer in a group.
Keep a clean camp. All food, and anything else that might attract bears & such should be kept well away from camp. Clean fish well away from camp. Any clothing that has the fish scent, or blood on it should be kept away from camp if possible. Sometimes when I'm backpacking, I have only one set of clothes and I'm not really into wandering around camp naked with my clothes 500 feet away, up a tree.
I do recall being a bit nervous after taking a nice bull elk, and getting all the meat down off the mountain and into camp. My partner slept with his .454 close to hand, and I kept my .44 and flashlight right next to my bag.
Tent or bivvy? Somehow that thin layer of nylon that a tent has seems to provide a bit of peace of mind. When I just lay there on the ground in my bivvy bag, I do feel a little exposed. Sort of like that old cartoon showing the backpackers all sleeping in their mummy bags and two bears looking at them saying "Look, tacos!" Is the tent really any safer? I don't know, but I sleep easier in it in the wilderness. Time to time though I save myself the weight and just use the bivvy bag - particularly in decent summer weather.
Bear spray - despite all the jokes - it has been proven effective. I've never used it, but am impressed with the stories about how well it can work. Will it always work? Nothing is "always" effective.
Bells on my pack - if not hunting, I don't mind making some noise while hiking through bear country. Again - lots of jokes about "dinner bells" as well as pepper scented bells in the bear scat... Yeah, okay. Good jokes. Still, a little man-made noise while hiking does serve to let the bear know you're approaching - avoids surprising the bear and scaring it into aggressive behavior.
A good stout handgun. Keep it with you. A friend of mine was making multiple trips on foot to set up his hunting camp. Came in with one load still on his backpack, and was charged by a medium size black bear in his camp. He shot the bear dead with his .45 sidearm. Was it a false charge? Was it the real thing? Who knows? He was told later by the game warden (yes he advised them that he'd had to kill a bear out of season) that there had been reports of a bear charging backpackers in that area. The backpackers would drop their packs and flee and the bear would enjoy the goodies he found inside their packs. Seems to me that the bear finally confronted the wrong backpacker!
I've backpacked, fished and hunted in grizzly and brown bear country too and have been advised by others who frequent such country to keep a good strong handgun with me at all times while doing so. A rifle has more power, but the handgun can always be on your person. Minimum that has been recommended to me while in bear country is a .44 mag with heavy bullets. In black bear country I feel adequately armed with my .357 mag, and it's a whole lot easier to carry. I've got a .500 S&W, but it's so bulky and heavy, I don't seriously consider hauling it along while backpacking. I'm usually trying to minimize the weight I carry, not haul along S&W's howitzer. Never shot a bear myself, so I'll defer all the arguments about which handgun and bullet combo to those who have. In grizzly country I carry a .44 loaded with 300 grain bullets. Seems a reasonable precaution.
Check in with the local ranger ahead of time. Is there a "problem" bear in the area? Might be worthwhile knowing...
Once, hunting and just bumming around in Wyoming, I came upon a series of drive-to campsites where signs were posted, advising that tents were not allowed, campers had to have "hard side" trailers to legally camp there - the grizzly problem in that area was well documented and folks were quite concerned about the big bruins. Locals advised against backpacking in and hunting alone. I took their advice and rented a small cabin as my hunting base. Asked how the locals hunt the area, and learned that they usually go in by horseback, in a group, and that having several hunters and horses tends to discourage bear trouble.
Hmmm. Typed too much. It's a topic that sparked my interest long ago and I've given it some thought over the years.