The answer for a big, fully crewed submarine is the USS Dolphin (AGSS 555), launched on 17th August 1968. Please see at the bottom for exceptions - small manned submarines. USS Dolphin (AGSS 555), homeported at the Naval Research and Development (NRaD) facility in San Diego, is the Navy's only operational, diesel-electric, deep-diving, research and development submarine. It can carry scientific payloads of over 12 tons, a considerably greater capacity than any other deep diving research vessel operating today. USS Dolphin serves as a scientific platform capable of operations at unprecedented depths greatly exceeding that of any known operational submarine. In November 1968, she set a depth record for operating submarines that still stands. In August 1969, she launched a torpedo from the deepest depth that one has ever been fired. The single most significant technical achievement in the development of the USS Dolphin is the pressure hull itself. It is a constant diameter cylinder, closed at its ends with hemispherical heads, and utilizes deep frames instead of bulkheads. The entire design of the pressure hull has been kept as simple as possible to facilitate its use in structural experiments and trials. Hull openings have been minimized for structural strength and minimum hull weight, in addition to eliminating possible sources for flooding casualties. General Characteristics Primary Function: Deep submergence research and development submarine Hull Number: AGSS-555 Class: No class; this is a one-of-a-kind ship Builder: Portsmouth Naval Shipyard Power Plant: Diesel/Electric; Two GM 12-cylinder, 425 HP engines Length: 165 feet (50.3 meters) Beam: 18 feet Displacement: 950 tons (965.25 metric tons) full load Diameter: 18 feet (5.5 meters) Operating Depth: 3,000 feet (915 meters) Submerged Speed: 10 knots (short duration), 3-4 knots (sustained) Scientific Payload: 12 tons + External Mounting Pads: 6 port, 6 starboard, forward and aft of sail Crew: 5 officer, 46 enlisted, and up to 5 scientists Operational Endurance: Over 15 days (for long deployments, Dolphin can be towed at 9-10 knots.) Armament: None Date Deployed: 17 August 1968 There is also a Russian oceanographer, Dr Anatoly Sagalevitch, who holds the world record for commercial submersibles: Dr. Sagalevitch's distinguished deep ocean scientific achievements have elevated him to international recognition as the top man in his profession. He has made significant deep ocean discoveries and his scientific accomplishments make him the premier diver for selection to receive the 2002 NOGI Sciences Award. He manages the operations of six manned submersibles and the largest oceanographic ship in the world. This energetic and ambidextrous man has conducted deep ocean scientific investigations involving scientists from Russia, the U.S., Canada, Germany, and Mexico; is the Chief submersible pilot and as a professional oceanographer he pursues his own scientific studies. He is at sea nearly six months each year. The National Geographic Society, NOAA, the Academy of Sciences of Mexico, and others have used his talent and facilities to support their highly successful exploration of the deep ocean. Highly productive deep submersible explorations, led by him, have included visits to the sea floor throughout the world?s oceans and seas. He has studied all six known types of hydrothermal vents. He has personally advanced our knowledge of deep sea floor ecology and the abyssal environment. This productive scientist is the author of more than 150 articles, books and scientific publications. This courageous man of the deep has established many records. Using the "Pisces VII", "Pisces XI", "MIR-1" and "MIR-2 manned submersibles he has been the leader of more successful deep submersible scientific expeditions than anyone. In 2002 he will add to the 2232 hours he has spent at depths greater than a mile. He established the world?s record manned submersible freshwater depth record of 5,310 feet, Lake Baikal. He was the first to successfully completed the sealing in of nuclear radiation sources on the sunken Russian submarine Komsolmolets at a depth of 5,600 ft. His expertise was also called upon to solve the cause for the Russian submarine Kursk sinking. He has been down to the HMS TITANIC 35 times for 465 hrs; another record. He pioneered the use of paired manned submersible diving and orchestrated the first rendezvous of two manned submersibles at15,000 feet! Since then this technique has been used on dives to explore the HMS TITANIC wreck site 12,500 feet down. Another first was his dedication of one MIR submersible to provide high intensity lighting for a second MIR submersible to photograph the entire TITANIC in IMAX, HDTV and 3-D video footage formats during the same dive series. The first deep ocean IMAX film 'TITANICA' established new IMAX attendance records in both the U.S. and Europe. This was followed by expediting acquisition of footage for the block buster movie 'TITANIC.' In summary he has contributed significant new knowledge about the deep sea through his personal investigations and his extensive cooperative research with other nations and entities. He has, throughout his career, demonstrated exceptional capability, dedication and professional acumen to ensuring safe scientific diving.

If you include all manned submersible vehicles, the US Navy bathyscaphe, Trieste, explored the bottom of the deepest part of the Ocean known, the Mariana Trench, with a crew of 2 on board. ( http://encyclopedia.thefreedictionary.com/Bathyscaphe%20Trieste ) The dive is recorded as over 35,000 ft (10,900 m) deep.

Since the question asks specifically for the depth record for a SUBMARINE, the answer is the Soviet K-278 Komsomolets, with a design operating depth of 1,250 meters (4,101 feet). However, the K-64, the first Alfa class submarine, reportedly reached 1,300 meters (4,265 feet). However, it is likely that stress cracking of the titanium hull forced an early decommissioning only a few years after she was built. The depth record for a submersible (NOT a submarine) is held by the Trieste, which dove the deepest part of the Mariana Trench at nearly 36,000 feet.

"The Trieste was a Swiss-designed deep-diving research bathyscaphe ("deep boat") with a crew of two, which reached a record-breaking depth of about 10,900 metres (35,761 ft), in the deepest part of any ocean on Earth, the Challenger Deep in the Mariana Trench, in January 1960." Source and further information: http://en.wikipedia.org/wiki/Bathyscaphe_Trieste "The deepest deep diving submarine to date is the Shinkai, which can dive to about 6,500 metres (21,000 ft)." Source and further information: http://en.wikipedia.org/wiki/Submarine Further information: http://en.wikipedia.org/wiki/Deep-submergence_vehicle