This is more of a brainstorming exercise than anything else but it is worth thinking about nevertheless.
1. China against the US - A war of ideology and Economic influences. Principal theaters of conflict would be the Pacific, South East Asia and Eastern Russia/Manchuria.
2. China allied with the Islamic World against the West - similar to scenario #1 but with more parties involved.
3. US against Russia - The original Third World as envisioned by Cold Warriors. Less likely to happen than in the time before the 1990s (collapse of Communism) but nevertheless it is still a possibility. Would be apocalyptic as both countries still possess the largest nuclear arsenals on the globe.
4. West and India against China and Russia - China and Russia fighting to avoid encirclement by their enemies. Could occur if Totalitarianism is resurrected in Russia.
5. US and China against India and Russia - Would be a possibility if Russia reasserted itself and realigned with India, Another Cold War Scenario come to life.
6. The Americas against Asia - A late 21st century war possibility that could occur as both continents strive for domination of the mining rights to the Planet's largest Ocean.
7. War of the Corporations - A war situation in a post-nation state world where corporations battle one another for control of the planet's resources. This war could quite likely move into the region of space near Earth.
8. The War of the Next ideology - A war in which the next counter-capitalism ideology raises its head, spreads out across the border and challenges the existing capitalist infrastructure. Counter-capitalism culture could take the form of rejuvenated Marxism or a totally new ideology (perhaps New Age) that has yet to be synthesized.
9. The Oil Wars - Decreasing energy resources may force the West to take matters into their own hands and force OPEC to hand over its assets.