With "big" bears in the equation, either my 30-338, or my 375 H&H.
If I were never going back to Alaska, and going to hunt the lower 48, first choice would be a 280 Remington, followed closely by a 30-338 mag or a 30-06. I could also live with a 6.5X55 Swede, a 7x57, a .308, a 270, 8x57, 7.65 Mauser, a 338-06. My lightest would be a 25 caliber ( 257 Roberts improved) and the heaviest would be a 35 caliber, 35 Whelen, 358 Winchester or a 9x57. If I could only have one it would all be about the rifle, how it was set up, and how accurate it was.
A good starting point assuming my first choice from above would be a Mauser or Sako action, 23 inch match grade barrel in a #4 to #5 Contour, with see through scope mounts and iron sights, a 2-7 power variable high dollar performance scope. Expedition grade wood very similar to the old Griffin and Howe stocks, pillar and glass bedded, blueprinted action, 2 1/2-3lb trigger, free float the barrel, English style butt pad, metal grip caps, swivel sling mounts, and a military style sling. From the bench I would expect .75"-1" groups with the right handloads and bullets, but would accept up to 1.5" groups with some of the premuim game bullets like 175 gr Noslers and such. With that rig I figure I can just about do it all, a tad light on the big stuff, a tad heavy on varmits with a 100 gr Sierras but I figure it would serve me well until something better came along. Besides that would keep me from horse trading guns every time I decided to hunt something different, which I would be very inclined to do if I could only own 1.