Up here in NW Montana, I buy all my guns with Survival Gun criteria in mind:
1. lightweight/ compact
2. reliability
2. versatility
If allowed just one gun, definitely my Mossberg 500 12ga pump w/ 18" barrel, rifle sights and sling. Super reliable and very light weight ~6.5lbs, and very handy at 37" overall. Has plenty of power with 3" mag slugs and quite accurate too. Good for taking any big game up to 100yds and the best for animal defense up here in grizz and lion country. This gun shoots a good birdshot pattern to only about 15yds with its cylinder bore but would do the job on most birds and ducks I put up.
However, In the same case as my shotgun, I always have my Ruger MKIII 22/45 with a 4" barrel and a red dot. This gun is reliable, easy to pack and shoots accurately: 2"groups at 40 yds+. The best for small game in my opinion. This two gun combo is the lightest, most versatile setup I have found. I will always have them together along with ammo and cleaning kit for an extended trip into the woods.
When I don't have space for the shotgun/.22 kit, I take my 4" S&W 629. So packable that it's hard to justify not having it at all times. It can take any game in North America with a well placed shot and .44 specials are good PD rounds too. This is an essential gun to have up here in the north country. I want to get a small Reflex style red dot for it to extend its range for better deer and elk capability.
I know many will say a red dot has no business being on a survival gun, but I have found them to be quite rugged on my .22, and extra batteries weigh next to nothing. Furthermore, I can always remove them and revert to irons if they stop functioning. It's just that I shoot so much damn better with them. The small ones like the new Burris Fastfire are super compact and won't impede its fast handling characteristics. Red dots simply add to a gun's inherent utility to me with little to no drawbacks.
Some links to local attacks this year alone up here. 1 lion, and 4 bear attacks. At least 3 other bear attacks I can think of, but no links to be found.
http://www.billingsgazette.net/articles/2007/11/13/news/state/44-mountainlion.txt
http://www.billingsgazette.net/articles/2007/10/31/news/state/27bearattack.txt