First post but, figured it was relevant.  I'm from the PNW Born/raised and Lived in NE Australia for several years working/fighting fire.  I'm also an avid Rafter/Back-country User/W-EMT etc. (I spend a lot of time out in the bush...) and have traveled up into CA/AK and had a LOT of encounters with Bears of both the Black and Brown variety.  Running is never a good option from the start as, like was mentioned, in that critical moment it makes the animal focus on you and make a decision, but 9 times/10 even a big Brown Bear is scarred to death of you unless they're "that Bear" (Animals have personalities as varied as people) or sick/injured etc..  Now all that being said, we're also driving animal populations crazy with all the developing/general parasitic Human growth and they can and will act funny when pressed into territory that's not familiar.   Thankfully I've never had to put one down, but that's what the Glock G20/Underwood Ext. Penetrator and some home-brew "Wilderness loads" are there for.  I'll also say that poorly trained/controlled dogs can make a bad situation with an unknown animal WORSE as they can drive them into a defensive posture instead of just scarring them away.  If the animal has nowhere to "run" it's likely going to come through you even if only to get away so being able to heel/control your dogs (something every dog owner should be able to do anyway... so sick of all these yuppies/idiots with their "fashion" working/big-dogs that don't socialize them well/train them/work them and then get mad at the dog for being "bad"... but that's another thread all together) and assess the situation is paramount and "creating calm" (if possible) is always best before you try to get big, make noise and look scary. Bear-Bells are a MUST IMO, if you're going into known territory, unless you're LOOKING to for the bears.   Warning shots can work as well, as a last resort IMO, but for I've also seen idiots rip off "warning shots" that were actually pointed down the trail or in general somewhere they weren't sure was clear/at the unknown and could just have easily hit another person as scarred the animals off... I actually find Black Bears, in certain areas like the Rogue River Valley here in OR for instance, to be more difficult to judge as they're subject to a LOT of poor behavior from River/Trail users who leave food out and litteraly try to treat them like pets or at least animals in a zoo.  Such a stupid idea and one that leads to the poor animal being branded "aggressive" when, once again, it's an idiot human factor being imposed on an animal.  FWIW, if you really want to feel the icy cold in your veins pay more attention in those "remote" beautiful areas and if you see/experience a Cat encounter you'll know what I mean... On land, nothing is as amazing or deadly/scary to behold as a Big-Cat in the wild and I've had a few close calls there too but luckily... I've still never had to kill any to save myself and I hope I never do. 

Cheers and No Worries

Dave

PS, Love the forum, glad to be here and really liking what I've seen thus far.  Much thanks to those who allow us to have such a place to come discuss these things and our 10mm Firearms esp.