Submarine Combat Since WWII
One of the comments in an earlier post asked if I had every been on a sub that had fired a torpedo in anger. The answer to that is "no"; I spent the 1991 Gulf War defending the coast of Delaware, and the Kosovo War and major combat portion of the Iraq theater of the Global War on Terror in new construction boats in Connecticut. Beginning with USS Pittsburgh (SSN 720) and USS Louisville (SSN 724) firing Tomahawk missiles during the 1991 Gulf War, several U.S. and British submarines have fired Tomahawks, mostly at Iraq, but also at the former Yugoslavia. I have not been on any of these boats.
With respect to what submarines are most famous for, which is sinking other ships with torpedos, this is not as common as many might think. Here is a list of all U.S. nuclear-powered submarines that have sunk enemy warships with torpedos:
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That's right, zero. We should be happy for this; any war in the last 50 years that would have involved submarines firing torpedos is a war we are happy to have avoided. Now, there have been many ships sunk by U.S. fired torpedos as part of planned exercises; WillyShake linked earlier to some good shots here. Some more pictures can be found as part of articles here, here, here, and here. (Submariners live for this stuff.) The only case I can remember of an American submarine sinking a ship with a torpedo not as part of an exercise was when USS Bremerton (SSN-698) sank the oil tanker New Carrissa off Coos' Bay, Oregon, when she had foundered and was leaking oil, on March 11, 1999.
In fact, I can only think of one instance when a nuclear-powered submarine sank an enemy warship with torpedos -- HMS Conqueror sank the Argentine cruiser General Belgrano during the Falklands War in 1982. Among non-nuclear submarines, the only post-WWII sinking of an enemy ship I can recall is when the Pakistani submarine Hangor sank the Indian destroyer Khukri during the 1971 India-Pakistan war.
While submarines may not have been sinking many enemy warships during the Cold War and beyond, their lethal potential was one factor that I believe helped keep the peace.
Update: bothenook has a post that shows American nuclear boats have done some damage since WWII...