Part of the Cold War era was hunting Subs under the Arctic ice, which is shallow water in many places. You can still torpedo a ship from periscope depth also. In addition, Satellites cannot remain on station 24/7, and UAVs are restricted by airspace and radar.
As the US Navy puts it -
http://www.navy.mil/navydata/fact_display.asp?cid=4100&tid=100&ct=4With the number of foreign diesel-electric / air-independent propulsion submarines increasing yearly, the United States submarine force relies on its technological superiority and the speed, endurance, mobility, stealth, and payload afforded by nuclear power to retain its preeminence in the undersea battlespace.
There are three classes of SSNs now in service. Los Angeles (SSN 688) class submarines are the backbone of the submarine force with 45 now in commission. Thirty-one Los Angeles class are equipped with 12 Vertical Launch System tubes for firing Tomahawk cruise missiles.
The Navy also has three Seawolf class submarines. Commissioned on July 19, 1997, USS Seawolf (SSN 21) is exceptionally quiet, fast, well armed, and equipped with advanced sensors. Though lacking Vertical Launch Systems, the Seawolf class has eight torpedo tubes, which can also fire Tomahawks, and can hold up to 50 weapons in its torpedo room. The third ship of the class, USS Jimmy Carter (SSN 23), has a 100-foot hull extension called the multi-mission platform. This hull section provides for additional payload to accommodate advanced technology used to carry out classified research and development and for enhanced warfighting capabilities.
The Navy is now building the next-generation SSN, the Virginia (SSN 774) class. The Virginia class is tailored to excel in a wide range of warfighting missions. These include anti-submarine and surface ship warfare; special operation forces; strike; intelligence, surveillance, and reconnaissance; carrier and expeditionary strike group support; and mine warfare. The Virginia class has several innovations that significantly enhance their warfighting capabilities with an emphasis on littoral operations. Virginia class boats have a fly-by-wire ship control system that provides improved shallow-water ship handling. The class has special features to support special operation forces. The torpedo room can be reconfigured to house a large number of special operation forces and all their equipment for prolonged deployments and future off-board payloads. The class also has large lock-in / lock-out chamber for divers. In Virginia class boats, traditional periscopes have been supplanted by two Photonics Masts that house color, high-resolution black and white, and infrared digital cameras atop telescoping arms. With the removal of the barrel periscopes, the ships’ control room has been moved down one deck and away from the hull’s curvature, affording it more room and an improved layout that provides the commanding officer with enhanced situational awareness. Additionally, through the extensive use of modular construction, open architecture, and commercial off-the-shelf components, the Virginia class is designed to remain state of the practice for its entire operational life through the rapid introduction of new systems and payloads.