The lead boat of the Thresher Class (later renamed Permit Class after Thresher's loss), the USS Thresher (SSN-593) was the first nuclear submarine lost at sea. Her loss was a watershed moment for the US Navy and led to the SUBSAFE certification program. Since the implementation of SUBSAFE, only one US Navy submarine, USS Scorpion (which was not SUBSAFE certified), has been lost.
Interesting side note: The Navy used oceanographer Robert Ballard's search for the RMS Titanic as cover for a mission to map and collect visual data on the wreck sites of both the Thresher and Scorpion. Ballard then used the same search method he had employed on the wrecks of the two subs to successfully locate the Titanic in 1985.