My father, who's now in his 60's, still hunts with a Winchester 30-30 that has been in our family since the turn of the last century, originally bought by my great grandfather. Loaded with 170 grain flat nose bullets, it has accounted for every one of the game animals listed, except for the brown bears. To the best of my knowledge, my father has never hunted with any other rifle, and I've never seen hiim shoot an animal more than once, but he does try to get pretty close before he shoots.
As for me, my first rifle was a Winchester 88 in 308, and it would also work just fine for anything short of the big bears if you loaded it with 165 or 180 grain Nosler Partitions. At least, that's been my experience.
For big bears, I'd probably take a 444 loaded with 310 grain WNFP cast bullets. I'd be just as happy with a 358 in a Savage 99, Winchester 88, or BLR, as long as it was loaded with 225 or 250 grain partitions.
