A total of 8 known nuclear submarines have sunk (all but one due to accidents) in the almost 55 years since they were created.
U.S. NAVY
USS Thresher (SSN-593) - Thresher-class (lead boat) Fast-Attack. April 10, 1963, during sea trials off Cape Cod. Major hull valve failure, leading to the SUBSAFE program.
USS Scorpion (SSN-589) - Skipjack-class Fast-Attack. May 22, 1968, returning home from Med deployment. Suspected torpedo hot-run incident and subsequent detonation before disarming.
SOVIET NAVY
K-27 - Experimental Soviet Fast-Attack, (2 lead-bismuth reactors in a modified November-class hull). Scuttled after a reactor control rod failure in the Kara Sea, September 6, 1982, in violation of International Regulations.
K-8 - November-class Fast-Attack, sank April 11, 1970 while being towed in rough seas following a major onboard fire.
K-219 - Yankee I class Ballistic Missile submarine. Sank East of Bermuda on October 3, 1986 while being towed after suffering major casualties and damage following an onboard missile explosion.
K-218 (Komsomolets) - Mike-class Fast-Attack, sank April 7, 1989 following a major onboard fire.
RUSSIAN NAVY (Post USSR)
K-214 (Kursk) - Oscar II class Fast-Attack. Sank August 12, 2000 in the Barents Sea following multiple onboard torpedo explosions (one triggered 2 others). The Kursk is the only nuclear submarine to sink after suffering major damage and later be salvaged. The History Channel and Discovery Channel often show documentaries on the raising of the Kursk.
K-159 - Decommissioned November-class Fast Attack. Sank August 28, 2003 after she broke from her mooring pontoons.
All boats are periodically checked for radation leakage of any type (reactors or weapons) and for any evidence of wreck tampering / attempted salvage. Most of the wrecks are in waters deep enough to preclude any salvage or tampering though.
A number of nuclear submarines sank, and the circumstances vary from accident to accident. Wikipedia has a list, and by going there and entering "List of sunken nuclear submarines" you can review that list.
52
52 u.s. subs were sank
Only one US submarine sank in World War One.
52 US subs were lost in WWII.
American submarines sank Japanese merchant ships.
Almost certainly a great number of sausages sank with the Titanic, but nobody will ever know how many!!
German submarines sank an enormous amount of British and Commonwealth shipping in the Atlantic and for a time in 1916 food stocks in Britain were down to about six weeks' supply. German submarines aslo sank some neutral ships and by sinking American ships they brought the U.S. into the war.
American citizens died when German submarines sank European ships.
During WWII the Finnish navy operated five small submarines, all designed in the Netherlands (by a Dutch front company) and built in Finland. Between them they sank one Soviet merchant ship and three Soviet submarines. All Finnish subs survived the war.
The Confederacy led in the experimentation with submarines. The most successful was the HL Hunley. This submarine sunk a Union warship however the sinking ship damaged the submarine that also sank.
No