Donkey Kong was highlighted as one of the first examples of Nintendo's overuse* of the "Damsel in Distress" trope in the first episode of Anita Sarkeesian's series on the portrayal of women in video games: https://www.youtube.com/watch?v=X6p5AZp7r_Q Very cool to see a parent help try to correct that for their kid as they introduce them to video games. *changed wording for clarity
Overused? This is the first Nintendo game that ever used that trope. Mario wasn't even called Mario before this point, and there was no princess. It was just Jumpman (renamed to Mario starting with this very game, who got his name from one of Nintendo's landlords at the time), Pauline (who got her name from the wife of an employee, but just "Lady" in the J version), and Donkey Kong.
While in the video Sarkeesian goes through its overuse in general as mturmon mentioned, Nintendo did go on to overuse it themselves, with Donkey Kong being the first of many times Nintendo went to that well. The linked video goes through several examples.