Nuclear war is probably the cause of most "traditional" P-A worlds. Nuclear bombs are among the most powerful weapons we have, and fallout from radiation can keep doing damage even after the bomb itself is long gone. Typically, an escalation in hostilities results in two major countries (the US and usually Russia or China) lobbing bombs. The rest of the world joins in, and pretty soon most major cities have been blown up and the surrounding areas irradiated. Radioactive fallout blows across wide swaths of land, killing and mutating as it goes. Sometimes there is a nuclear winter, where dust in the atmosphere cools the planet and causes an extended winter. Survivors of the initial war take refuge in bomb shelters and bunkers, sometimes for generations. Remnants of technology are here and there, but between the destruction and the passage of time, examples of advanced technology are few and far between. There are usually some fanciful mutant humans and animals too, caused by exposure to radiation.
One of the things I like about the nuclear P-A world is the fight against the environment, which seems to be more important than in some other types of P-A worlds. Radiation in high enough doses kills pretty much everything, and finding uncontaminated food and water is a major task. Large irradiated areas prevent movement across country. Radiation is also somewhat mysterious, an invisible foe and difficult to deal with. There is also a popular tradition of radiation causing viable mutations which makes for some interesting obstacles in the new world.
The classic computer RPG Fallout and its successors take place in a nuclear P-A world inhabited mostly by human survivors, but also by mutant humans called ghouls and super-mutants. High technology is usually military in nature, and the pre-apocalypse technology level included energy weapons, power armor, robots and fusion powered cars, to name a few examples. The games don't focus much on survival but more on combat and interaction with the small towns and villages trying to deal with the bad elements of the world, mostly roaming gangs and mutant menaces. Fallout 3 is in the works, and will have more survival elements, like radiated water. You'll need to drink water occasionally, but most of the water you find will be slightly irradiated, so you'll have to balance the two factors. You can find more about the Fallout series at the fan site No Mutants Allowed.
The book A Canticle for Leibowitz is a more serious fictional look at dealing with the recovery of civilization after a major nuclear war. After the war, the survivors rebel against technology and science and send the world into a new dark age. An order of monks hides and preserves books for future generations so that they can recover the science and technology of the old world. The idea of the monks preserving valuable books is one of the things that inspired me to start the Post-Apocalyptic Survival Bookshelf. Canticle deals with a lot of interesting issues, like faith, knowledge and power, but only the first third of the book really deals with the kind of post-apocalyptic world I'm interested in. During the other two thirds civilization has recovered to the point that they are no longer fighting against the environment, but merely other civilized humans.
What are your favorite nuclear themed P-A worlds?