Russia and the US have something like 5000 nukes each. Many if not all of those nukes are way more powerful than the ones that flattened Hiroshima and Nagasaki.
Even if only a small fraction of them make it, they'd likely be enough to completely destroy every major city in both countries... and cities are where almost the entire population lives. Plenty of remote areas will likely be hit too, because that's where the missile launch sites and military bases are.
All those huge "impregnable" bunkers you see in movies that were supposed to house governments in case of nuclear war were quietly decommissioned because it was realized that they couldn't survive hits from modern nuclear weapons and there's no way to hide them from today's surveillance technology.
So in an all-out nuclear war probably most everyone in Russia and the US would die from direct hits.. and that doesn't include knock-on effects from radiation poisoning and fallout, nuclear winter, complete infrastructural and governmental collapse (ie. no clean water to drink, all the animals dead, no food and perhaps even no ability to grow food).
As for other countries, I'd read that after the fall of the Soviet Union, the UK general in charge of his country's nuclear arsenal met his Russian counterpart and him whether he thought the movie Threads was an accurate depiction of what would happen in a nuclear war between the two countries. The Russian general laughed and said the entire UK was designated an overkill zone.