I read somewhere that a 10,000 megaton fission-fusion (Hydrogen) bomb would, if placed well, destroy all higher forms of life.
The Earth would be populated by bacteria, cockroaches, Republicans and Jehovah's WItnesses... New World Order ugh!
However, no one's ever made a 10,000 megaton H-Bomb; the very very largest are a handful of megatons, and most nuclear devices are in the kiloton range.
At the height of the Cold War, if there had been a full launch by the USA, UK, France (god know where they would have aimed theirs), USSR and China... well, our grandchildren would be getting aid parcels from the Southern Hemisphere, and would be able to open them with their toes.
Put less cryptically, there would be massive initial casualties, 100% in many major cities, near to 70% for most Western nations, with another 10-20% dying in the next week. The 5-10% that would survive longer term would probably all suffer short and unpleasent lives, and have massive genetic damage to pass on to their children. If conditions allowed a 'nuclear winter' to takle place, loss of life would be massive and worldwide.
Nowadays this is all very unlikely, and nuclear arsenals are not what they used to be. The USA could effectively end civilisation in whatever country they chose, China and Russia too. The Ukraine, France and the UK could take out major bases and cities, but the risk of nuclear war obliterating most life in one hemisphere (and severly damaging the biosphere in general) is practcally nil; there's nothing in it for anyone.
Israel could and would obliterate the Middle East if they were going down, but would probably destroy the capitals of their enemies well before that, as well as airbursting above any troops headed their way. Pakistan and India could cause huge problems politically speaking, but their nuclear weapons would only have limited effect outside of those countries.
Terrorist use of nuclear weapons could kill humdreds of thousands and put the targeted city centre off limits for quite some time; it's quite hard to make a nuclear bomb go bang, but you don't need that much Physics to make a sub-critical pipebomb (which would be like a massive incendary device), or have radioactiove waste as the 'shrapnel' of a large conventional bomb.
So, bottom line; yeah, in a imaginary scenario it could happen, but there aren't really enough bombs anymore, a full-scale lauch is unlikely to happen, and minor nuclear wars/terrorist use of nuclear weapons, although destressingly possible, would only really effect you if you were in the wrong place at the wrong time...
... of course, if a terrorist nuclear device DID go of in the US, I think the Patriot III Act would effectively curtail many freedoms in the name of security. A kinder, gentler, machine-gun hand...