Yeah, the world probably isn't doing so hot, in whole or part. My command of the lore isn't outstanding, but most (if not all) regions fell into internecine strife during the resource wars and they'd probably torn themselves up pretty badly before the bombs even had a chance to drop. When the war did go hot, I'd imagine that few places were spared, as there were plenty of nukes to go around and there would be military targets and potential hidey-holes and resource reserves on every continent. If you're fairly certain you're going to be mostly obliterated, your only real option left is to make sure you wipe out any potential competition for postwar revival on your way out. It's the dark obverse of the mutually assured destruction policy.
America and China are probably doing better than most places because being the last societies with resources to spare means there are more goodies kicking around for the survivors to find, but that could also mean that areas that have had to fend more for themselves and had less access to prewar weaponry have developed more stable and wasteland-savvy communities.
Resource hubs were probably heavily militarized by their local or colonial despoilers in the days before their depletion, and if any of them escaped targeting they'd be prime sources for regional powers to spring up from.
I doubt many populations would have been totally wiped out-- we know Mexico fared decently, and if the neighbor of one of the biggest targets of the war can make it, there's hope for almost anyone. I think it would kind of go against the 50s/80s ideal of total nuclear annihilation if any area much larger than Vegas or Zion Canyon managed to survive unscathed, though.
Then again, even the original devs (original enough, anyway-- the good Messrs. Sawyer and Avellone) have been moving away from the pulp-sci "absolute" wasteland ideal for the setting and beginning to alloy it more with "real-world" science and logic, with numerous suggestions in NV and its DLC that there were sizable groups of people who managed to survive outside the vaults, so who knows? Maybe there are whole island nations that didn't get hit, though without resources of their own or anybody to import from I imagine they would have backslid rather quickly into tribalism or something resembling it.
Anyplace that might have survived wouldn't have been able to support modern-age population figures, and they likely would have lost most of their most specialized (and technically valuable) citizens in the die-off. Most populations wouldn't largely be in possession of the knowledge and skillset necessary to adapt to the new world, which might leave traditionally poorer and less advanced areas with a distinct advantage.
... I'd close by asking your forgiveness for a lack of coherent organization here. It's late, I've got a very high fever, and yes, I'm aware that this is a bit long in the tongue even for me.