The increase in numbers of airplanes flying over the united states prompted the creation of demarcations on airspace, to provide for better traffic management and ensure the safety of all aircraft involved.  The following classifications are determined and regulated by the FAA and enforced via the several Air Traffic Control Centers throughout the US.

Class A Airspace

Extends from 18000 feet to 60000 feet.  All aircraft in this zone must adhere to Instrument Flying Rules (IFR) and must file a plan accordingly to the appropriate ATC and receive clearance for it.  They must also reset their instrument so that all the aircraft will have the same reading on their altimeters to ensure proper separation.  This airspace affect all 48 contiguous states and 12 nautical miles

Class B Airspace

Extends from the surface to 18000 feet.  This is most often modified to meet the needs of the airports it surrounds.  In order to enter Class B airspace, all aircraft must receive clearance from ATC and strictly stick with the heading, altitude and speed assigned to them for safety, since it's usually the busiest and most crowded.

Class C Airspace

Only found in airports that have an operating tower and can be serviced by radar approach control and support IFR operations.  It is individually tailored to meet the needs of airports.  Pilots must establish and maintain two way radio communications at all times with ATC controllers until they are handed off to the tower for landing.

Class D Airspace

Goes from the surface to 2500 feet above certain airports.  It is necessary to establish two way communications with ATC, although  no separation services are provided to aircraft flying under Visual Flying Rules (VFR).  It is also present in uncontrolled airports (without a tower).  In this case, a broadcast frequency will be used for pilots to inform other aircraft of their intentions (such as, landing, departing, etc.)  Responsability for aircraft separation falls in the hands of those flying the planes.

Class E Airspace

Controlled airspace that does not falls into the previous categories is called Class E.  It is usually used when transitioning between other controlled arieas under IFR.  VFR planes can use this airspace so long as they can mantain VFR conditions for separations, and olny up to 17500 feet.

Class G Airspace

This is uncontrolled airspace.  IFR doesn't operate here.  VFR planes can operate in this airspace if weather conditions allow for it.

Sources: FAA web site.
Airspace Classifications.