11:08 p.m. on April 2, 2009 (EDT)
I have no experience with grizzlies, only experience in areas with lots of black bears, mostly small to medium size, just to be upfront about it.
My own experience has taught me this:
Depends on the Dog owner, the dog, the breed, how much training & what kind, the circumstances, and so on.
I have had several dogs that I hiked and camped with.
My current dog is an Akita, very well trained specifically as a pack dog to go with me on solo backpacks. My dog carries a pack and hauls his own gear and some of mine. This is my third pack dog, and here are a few things I have learned, some the hard way. I am no expert, but had expert help with training the dog.
Untrained, off leash dogs are quite frankly a public nuisance in the back country, running around chasing critters, running past people on the trail, barking, making other hikers nervous, etc.
Dogs on leash, with some training, are a little better, but if not accustomed to the outdoors the training usually goes out the window quickly once on the trail.
A well trained dog of suitable breed, accustomed to hiking or backpacking, and of the right temperament can be a great companion for someone who is willing to put forth the effort required. Dogs are almost always cheerful, alert,ready to go, loyal, don't complain, don't repeat stories, etc.
However dogs are governed partially by a set of instincts that causes them to do things that at times may not be in your best interest, if you understand that and have control of the dog, and can manage the dog from a distance by voice command (not yelling and screaming) then you shouldn't have any problems. I say "from a distance" because this should be the standard by which your dog is trained, on leash dogs are easy to control, but if your dog is off leash, even accidentally, you should still be in complete control. If this is not the case, more training is needed before your dog is ready, or you don't have the right dog for the application.
As far as protection from bears, dogs are not a match for bears physically. Your dog may not understand that! The same can be true for some of the larger critters like skunks, marmots, raccoons, & snakes if your dog corners them. This is where their instincts can cause a lot of unnecessary trouble for both you and others around you. Your dog should be trained to stay by your side even off leash, alert, but restrained in terms of temperament. This is where picking the right breed, and the right conditioning early on is so important. Certain breeds can stand their ground to a point, and can add a significant deterrent to any further advance by a bear. Any aggressive advance by the dog, or the dog giving chase to the bear will only agravate the situation. I would point out that this is my opinion, others hold a different view. Lots of people in more remote areas do use dogs as a deterrent, but not just any dog you happen to have is suited to this. I would also point out that I do not consider this to be my dogs role, although his size and temperament is suitable for that application.
If the breed you choose loves to give chase to other animals you may have nothing but trouble. I would not consider any dog from the Hound, Terrier, or Herding groups. I have had best results with dogs from the Working group, and specifically those breeds that are sturdily built.
Dogs do posses abilities and instincts that surpass our human capabilities in certain areas. While the dog is a good companion, they are capable of being so much more, this aspect of having a dog with you can be quite rewarding.
You dog can play a very significant role if well trained, and, you are in tune with the dogs behavior, abilities, and body language. Dogs can of course, see, hear, smell, and sense things that we can't, or much sooner than we can. You should consider using the dogs abilities as trail tools to stay safe, rather than using the dog to defend you from Grizzlies or Woolly Mammoths in my opinion.
The dog can serve as sentry, their hearing and eyesight in the dark, coupled by their ability to detect motion should be used to inform you of what is going on around you, so that YOU can make intelligent, safety based decisions. Not so you can send your dog out as your first line of defense, and against what? Most times a Raccoon or other small critter just going about their daily or nightly routine. Or maybe a fellow hiker who is just passing close by.
Properly trained, and again the right breed, your dog should raise it's head and look intently in the direction of a sound, but NEVER bark, or go running off. The dog is to stay by your side, the dog is your tool. If you were hunting it might be different.
Entirely too many people think of a dog the way many people think of a knife. You know, must have the Rambo or large survival knife capable of felling trees, or skinning buffalo.
The well trained dog, like the right kind of knife, is a tool that, used properly, and with experience, can make life easier, safer, and more rewarding on the trail.
I would add that I take my dog mostly in more remote areas, and not on heavily used trails, I do whatever it takes to be considerate of other hikers. We yield the trail if we do encounter others, the dog is trained to sit quietly by my side as I greet the other party, seeing that your dog is well trained puts most people at ease.