*Technically, they're not acronyms, they're mostly initialisms. See here for clarification.
**See? There I go again!
Anyway, here's a quick list of the most common. I'll add to it later as more pop up.
- NATO- North Atlantic Treaty Organization: Pretty obvious really, but I put here for the sake of completeness. NATO (or OTAN, if you're French) is the international organization in charge of most of the foreign military forces in Afghanistan.
- ISAF: International Security Assistance Force: The operational arm of NATO, with about 60,000 troops, US and allies, managing security and counterinsurgency operations in about three-quarters of the country.
- ANA- Afghan National Army: Roughly 80,000 strong and growing, although of highly-variable quality and reliability. Some battalions are capable of independent, agressive operations, but many prefer to remain in their fortified bases and smoke massive amounts of hash.
- ANP- Afghan National Police: Probably the single-most reviled institution in Afghanistan, the police are really more of a paramilitary security force than an investigation and apprehension force. Not a bad thing really, since there are few courts and fewer jails to actually try, convict and imprison any common criminals. Noted for their penchant for demanding bribes. Also worth pointing out however, that the ANP lost more people in combat last year than the army.
- ABP- Afghan Border Police: A separate division of the ANP, the Border Police are responsible for monitoring the country's borders (a hopeless task), guarding the airport and much of the counter-narcotics work (another hopeless task). Surprisingly professional, despite the fact that they are trained under a program run by Blackwater.
- NDS- National Directorate of Security: A combination of FBI and CIA, the NDS are mostly former spies and counter-intelligence agents for the Soviet-backed government. Some flickers of professionalism, but vastly underfunded and not respected by the local population. They have a well-deserved reputation for brutality. Their independently operated detainment centers make Guantanamo Bay look like a health spa.
- HeI- Hezb-e Islami: The personal army and jihadist political party of Gulbuddin Hekmatyar, a former mujahideen leader and warlord. Some portion of the anti-government violence here is perpetrated by HeI.
- AQA- Al Qaeda in Afghanistan: A regional variation on AQI (Al Qaeda in Iraq). It's hard to deny that AQ once had a presence here, and they probably still do. Foreign jihadists, mostly Pakistani and Arabic, are sometimes caught or killed by ISAF forces, but the actual number of Al Qaeda operatives in Afghanistan is impossible to determine.
- ACE- Army Corps of Engineers: Not really part of the US Army anymore, these are the guys responsible for planning and building many of the large military infrastructure projects around the country.
- AFCEE- Air Force Center for Engineering and Environment: The other large agency responsible for planning and executing big building projects around Afghanistan, mostly military bases and airfields.
- CJTF-101- Combined Joint Task Force, 101st Airborne Division: The main US combatant command for all US troops not under ISAF control.
- CSTC-A- Combined Security and Transition Command, Afghanistan: The US Army command responsible for training and mentoring the ANA and ANP. These guys are spread out all over eastern and southern Afghanistan, embedded in small groups with local forces, working every day to make the locals better soldiers and citizens. A very tough job (and I ought to know).
- RCE- Regional Command East: One of four regional subcomponents of ISAF, RCE runs the American forces that do not fall under ISAF command. Operates, as the name implies, in the difficult and violent east of the country.
- USAID- United States Agency for International Development: The third of three big funders of construction projects. Mostly deals with economic infrastructure like roads, bridges, dams and irrigation.
- Taliban: Not actually an acronym (duh!), but also included here for the sake of completeness. The Talibs (pashto for student) are the chief badguys here in the -stan. Fundamentalist, Wahhabist Muslims (think revivalist preachers, but with more guns).
That's all I've got for now. There are dozens more, but as I read over what I've written already I realize that I might actually only be confusing people even more.