When the world goes to hell again, I've always predicted that the natural allies will stay true. I expect the countries of primarily English origin (America, Britan, Canada, and Australia primarily) to be the main block (and really, that's just about enough stuff to take on the entire world, assuming some other power was on there side (like Russia! Wouldn't that be a funny conflict). I could see the blocks being like this:
Allies: America, Britain, Australia, Canada. Various other small islands. Taiwan and South Korea as well. Easily the strongest power in conventional war.
Europe: Self explanatory (sans Switzerland and Lichtenstein).
Russia: Bit of a wild card. Could possibly be with Europe (making Europe the second major power). If they go by themselves (and possibly take a bit of Eastern Europe), they'd have a fair bit of power (especially if they took on 3rd world countries, they have enough material to do a lot, depending on mobilization).
China: Probably includes a fair bit of SE Asia. Possible cooperation with Russia. Opposed by the Allies and India.
India: Might be with the Allies, but I doubt this. If I had to guess, they'd be the epicenter of the conflict, possibly exchanging nukes with Pakistan over Kashmir.
Muslims: Interesting question. I don't remember which countries are Shi'ite and which are Sunni right now, but there'd be some chance of two powers on sectarian lines, or a smaller one of a pan-Arabic alliance. Relatively minor, although oil may be a factor. Expect Paki-Indian war and some tussles with Israel.
Israel: Probably going to have Allied support. Could start conflict via an attack on Iran (like they did against Iraq some time ago). Possible nuke use if attacked?
South America: I could see South and Central America getting together. They'd have a surprising bit of power (provided Venezuela doesn't throw a wrench into things. Venezuela or drugs are another possible spark, btw). I'd expect them to be with the Allies to some extent.
Africa: ATO (African Treaty organization) is a very real possibility from my standpoint. Expect it to be mostly symbolic in any case though. Africa has enough trouble keeping itself together on the state level, much less the country or continent one. Possible draw of other troops in Somalia.
At this moment, there are about half a dozen spots where trouble could start up. However, there isn't any spot for WWIII to start yet. As long as NATO remains strong, any major wars will be one sided, or very very bad (read nukes). However, if we go a few years in the future (call it 6? About when I hope to have a Tank Company), the situation can change. I foresee NATO dieing sometime, and Europe breaking away from US. China will continue to expand, as will Russia to a lesser extent. To my eternal chagrin, draw down will probably happen in the US. Fucking idiots.
Then, we just need a spark.
1) Taiwan. China invades the ROC. America comes to Taiwan's defense. Probably leads to a slaughtering of China, I'd expect Europe and Russia to come against the commies. If China was to have Russia on their side, and Europe were to stay mostly out of the fight, it'd get awkward. Especially because both sides of a hot war would have strategic nukes.
2) Korea. Same thing. North Korea invades and gets backed by China.
3) Kashmir. Pakistan and India come to blows. Possibly with nukes. The blocks go to one side or another.
Honestly, as far as I can tell, this is the only way we're going to get wars. However, there are a couple of other spots where I wouldn't be surprised if little wars fired up (of course, getting shot in a little war isn't that different from getting shot in a big one). Note that if the big one breaks out while these are occurring, a fair bit of the world's military (especially America) might be tied up
1) Israel. Repeat of the last one. Muslim vs Jew. If Israel looks like they're going down, expect US involvement.
2) Somalia. I could see another 'UN' mission there, with possible repeats of the Battle of Mogadishu. Could VERY easily result in the country getting blown to bits (let me put it this way, if I had been in charge during 'black hawk down' there would've been a lot of damage to the city.
3) Iran. Invasion over nukes. US cesspit when it isn't handled correctly.
4) Bosnia. Nasty UN mission?
5) Rwanda. See above?
6) South America. Venezuela does something REALLY stupid and gets invaded.
7) North Korea. Invades the RoK, but isn't backed by China. They get their asses kicked. Probably end of county if their stupid enough to try a nuke.
Middle East. Civil War somewhere?
9) Africa. Civil War somewhere?
The problem right now is that NATO and the UN still tilt things strongly to the status que. The UN doesn't seem to give a rats ass about internal things (it's not genocide, just racial cleansing, okay?), but they'd still get pissy if a country was actually invaded.