The Holland America Line ship "Prisendam" sank after a fire in the Gulf of Alaska in October 1980. Maxtone-Graham wrote about it in Liners to the Sun. [There is a new Prisendam. I would never name a new ship after one that sinks.]
This ship caught fire off the Malaysian coast. 1093 passengers and crew escaped in the ship's boats and liferafts. To my knowledge, this is the largest number ever saved from a sinking ship entirely by the ship's own survival craft and without loss of life.
Whether the singing of My Heart Will Go On helped is debatable.
Others include Royal Pacific on 23 August 1992 and Oceanos on 4 August 1991.
Quite a number of cruise ships have been destroyed or badly damaged while in port.