Special Forces.  Also known as the Green Berets, from their distinctive headgear.  The Special Forces are comprised of small groups of highly trained officers and NCOs, whose mission it would be to conduct "behind-the-lines" operations in enemy territory, for reconnaissance, target acquisition and damage assessment, and precision strikes on strategic targets.  SF units have another unique mission, and that is to train and operate insurgency and counter-insurgency units in the field, a mission they performed admirably in Vietnam. They are very well-schooled in foreign languages and customs, and are the units of choice when a training mission is done in another nation. For example, there are several SF units currently in Bosnia retraining the Bosnian military to fight conventional warfare. SF units were present in large numbers in Desert Storm and afterwards in Kurdistan.  Each of the Special Forces Groups listed below are specilized in a particular region, such as Latin America or Europe, and are all Airborne-qualified units.

 Rangers: Rangers perform more of the traditional raiding and commando-type missions associated with the popular image of SpecOps personnel.  Rangers are intended for deep, high-risk raids on critical objectives, and usually operate in battalion strength. They are well-trained, and extremely aggressive in combat. Rangers were given the highest-risk operations in Grenada, Panama, and Somalia conflicts. Rangers are all Airborne-qualified units.

 Special Operations Avation: SOCOM's private air force.  These are the highly modified aircraft that support the Special Forces and Ranger units.  Mostly, they are conventional UH-60 and CH-47 transports that have been modified for night/bad-weather operations, and given aerial refuelling capabilities.  One battalion is armed with light, "quieted" helicopters such as modified AH-6 Cayuses for gunship operations.

 Psychological Warfare: Or PSYOPS.  Not listed below, but important none the less.  These are the units that combat enemy minds, and performs anything from broadcasting loud rock music into enemy camps to distributing leaflets calling on enemy units to surrender.

 Civil Affairs: Also not listed below. One of the most unusual branches in the Army.  Civil Affairs units are the Army's way of interfacing with civilians, either foreign or American.  CA units are those that work with local governments to get access to supplies and support while US troops are "in-country."  They also handle the civilian news media, controlling what news gets out and what news doesn't.

  1st Special Operations Command (1st SOCOM) Headquarters: Ft Bragg, NC
History: Formed in the 1980s as a overall command unit for Army special operations, 1st SOCOM is the only higher command for Special Forces, Rangers, and the others.  1st SOCOM does not command units in combat theatres (that is left up to the theatre commanders) but trains units for upcoming actions and plans special ops actions.  Special Operations personnel are often looked down on by other combat arms, but it is not the limited carrer path it used to be: the current Chairman of the Joint Chiefs, Gen. Henry Shelden, is also a Green Beret.
Current Status and Deployment: 1st SOCOM units are deployed worldwide on a wide variety of missions.  Mostly these are assistance to other governments, such as Special Forces training teams and Civil Affairs teams.  Given how active US foreign policy is, it's probably a given that there are at least some SOCOM units on a "black" (secret) mission somewhere at any given time.
 

Special Forces units

All Special Forces battalions belong to the 1st Special Forces Regiment

other Special Forces units

Special Forces Detachment Delta
Location: Ft Bragg NC
This is the famed "Delta Force", comprise of Special Forces personnel, and supposedly the primary Anti-Terrorist unit of the US Army.  Much is rumored of this unit, but very little in the way of actual operations has actually been confirmed.

National Guard Special Forces
The National Guard also operates Special Forces groups, to back up the regular forces and form a pool of skilled personnel in time of emergency.  The reserves form the majority of PSYOPS and CA units as well, although they are not listed here.

 19th Special Forces Group (Airborne) (UTNG)
 20th Special Forces Group (Airborne) (ALNG)
 

Ranger units

Other Special Operations units