Successor to the Neptune P2V and developed in the late 1950's, the P-3 is the current primary patrol and long endurance ASW platform fielded by the United States Navy. The aircraft originally was manufactured as the P-3A, essentially a shortened civilian Electra airliner with increased fuel capacity and the ability to carry various ASW weapons. The aircraft is named Orion for the Greek god of hunting.

P-3B 'Iron Clad'
The P-3B first appeared in 1981 with the code name CLIPPER TROOP WEST. Significant variations between the P-3A and P-3B include the addition of infra-red imaging systems and a nearly four-fold increase in acoustic processing capability over the previous model. The first four LRIP (Low Rate Initial Production) models were subsequently assigned to VPU-1 (Patrol Squadron Special Projects Unit) in Brunswick, Maine and VPU-2 in Barbers Point, Hawaii. (Note: VPU-2 has since relocated to MCAS Kaneohe Bay, Hawaii following the BRAC closure of Barbers Point in the late 1990's.) This variant of the P-3A was then further modified with specific equipment enabling it to pursue an ELINT/MASINT/COMINT mission. Redesignated as the P-3B the aircraft continue to this day as the primary long-range intelligence collection sensor platforms used by the United States Navy. Operational details concerning the nature of P-3B deployments and activities are scarce considering their missions, however they have been known to perform photographic reconnaissance of high interest targets and sensor surveillance of ballistic missile launches. Some research indicates that a handful of P-3B airframes have been modified to carry SMILS (Sonobuoy Missile Impact System) equipment to aid in a MASINT mission profile.
Since 1996 and the phasing out of the P-3B platform, VPU-1 and VPU-2 are now purported to field only specifically modified versions of the EP-3B depending on mission requirements. Unpublished modifications to the aircraft are routinely made by maintenance personnel serving at these two squadrons to accommodate given sensor packages.
Aircraft from the two publicly active special projects squadrons are rumored to change BUNO (aircraft serial) numbers, squadron markings and identifying marks when operating outside of the United States. (Note: the author has spoken to at least one reliable anonymous source that indicated this was indeed true.)

P-3C
In it's present vanilla ASW incarnation the P-3C has superceded and replaced the older P-3A models. The aircraft is 33.8 feet high, 167 feet long with a 99.7-foot wingspan. Power is provided by four turboprop engines coupled to variable pitch propellers of the same type as the C-130 Hercules. These aircraft carry MAD (Magnetic Anomaly Detection) equipment for detection of underwater disturbances in the Earth's magnetic field. Plans to upgrade the existing AN/APS-115 surface search radar to the AN/APS-137 Inverse Synthetic Aperture Radar) were delayed due to funding constraints in the late 1990's Clinton military budget. However the upgrade continues to be integrated into the fleet, giving the airframe the ability to take strip pictures of given targets via radar imagery. The P-3C has an average endurance capability of 16 hours, a range of 4,500 NM and a service ceiling of 28,300 feet. There are numerous squadrons that operate this aircraft from nearly every significant U.S. Navy installation in the world. Primary bases include Misawa and Kadena AFB in Japan; NAF Keflavik, Iceland; NAS Rota, Spain; Ascension Island; Diego Garcia; Anderson AFB, Guam; MCAS Kaneohe Bay, Hawaii; Lejes air base, Azores; Bermuda and Puerto Rico.

P-3C BEARTRAP, EA-3B, EP-3E
Initially five P-3C airframes were modified for the purpose of recording high-fidelity audio of then Soviet equipment. These aircraft were known by the codename of BEARTRAP and were upgraded in 1994 for a mission expansion into the littoral and regional environments.
Another further modification of the P-3A comes in the form of the EP-3 ARIES and ARIES II which have been significantly modified for the purpose of intelligence collection. Altered statistics of this airplane include a four-hour reduction in endurance and a 500-mile reduction in maximum range. Targets of the EP-3E include ELINT and COMINT targets of interest with occasional forays into MASINT. Two squadrons currently operate the EP-3, VQ-1 of NAS Whidbey Island, Washington and VQ-2 of NAS Rota, Spain. SIGINT missions flown by VQ-1 in the Far East (including the South China Sea and the Sea of Okhotsk,) are designated BEGGAR SHADOW, BEGGAR HAWK and BEGGAR WATCH. Western European missions flown by VQ-2 are designated FLOOR DOOR (COMINT) and FLOOR LEADER (ELINT.)
Specific sensors peculiar to the EP-3E ARIES II include the readily identifiable dorsal 'canoe' structure housing an AN/OE-320 DFG array for the purpose of locating transmitted signals. Another large ventral radome beneath which lies the antenna for the AN/OE-319 radar is also readily identifiable in even rough pictures of the airframe. This variant aircraft is also carries a significant amount of equipment for the analysis of communications intelligence, electronic warfare and electronic intelligence.

Sources:
The U.S. Intelligence Community, Third Edition: Jeffery T. Richelson, 1995. (Westview Press)
http://www.janes.com/aerospace/military/news/jema/jema010402_1_n.shtml, Janes ARIES II information.
Private materials and spoken discussion: Yurei, 1998.
Thanks to baffo for finding the ARIES II information and sending it this way.