"Rapunzel" is actually an inversion - the prince does not rescue Rapunzel, he just gets her pregnant, and later on it is her tears that cure his blindness. Also in "Little Red Riding Hood" the eponymous character is too young and the grandmother too old to be really considered a damsel in distress and that the story originally ended unhappily, getting two endings tacked on later (first the wolf being killed by the passing huntsman, later the cutting-open and revelation that the Little Red Riding Hood and granny had survived).
In "The Young Slave", the heroine is the illegitimate niece of a lord, whose wife finds her in enchanted sleep and, in a fit of jealousy, beats her, knocking loose the comb that had kept her asleep, and turns her into a slave, abusing her so severely she thinks of killing herself. One day, her uncle hears her lamenting her woes and saves her.
In "The Grateful Prince", the king promises his baby to an ogre, and so takes a peasant girl and leaves his son with peasants. The ogre takes the girl and leaves, but the boy, on growing up, decides he can't possibly live on such a sacrifice and goes to rescue her.