Every scramble in 14 years of UKSAR was a memorable flight, from premature babies to heart attacks, cliff-stickers to mispers, drowners to cliff-fallers, sinking boats to kiddies on lilos - even some of the searches were memorable, especially when you actually find the person you were looking for!
Best job in the world.
Outside of that - the moment when your student suddenly gets it - after mistakes and frustrations - when you finally push the right button to make them understand the often complex skill you are trying to impart.