While our capable medievalists may be able to provide an example of a real instance of the rescue of a lady imprisoned in a dungeon/tower, we need to consider the very real third possibility: Disney was not the source of this sort of story. Instead, Disney borrowed from folktales, the adult, fictional folk literature of the pre-industrial world. Many folktale types include this motif, and Disney found in this body of material ample inspiration for his movies. One can argue that many of these stories are either medieval or late medieval, so although they may not be based on actual events, they were very real period stories, the literature of the illiterate folk.
This kind of thing comes directly from medieval chivalric romances. It's all over the place in Malory's Le Morte d'Arthur, which is basically the last and best of all medieval chivalric romances.
See, for example, the story of Elaine of Corbenic: she was cursed to live in a bathtub full of boiling water (and not die). Lancelot broke the curse, and she fell in love with him. He still loved Guenevere, though, so she tricked him into sleeping with her--from this union Galahad was born.
Then of course there is the story of the Knight of the Cart. The thoroughly unpleasant and creepy Sir Meliagaunt kidnaps Guenevere and her attendant knights (they were unarmored at the time, and she surrendered so they wouldn't be killed defending her). Lancelot, of course, goes to rescue her, but his horse is killed so he rides on a cart.
Besides that, there are various incidents where a particularly bad knight locks people up for no good reason. Often this will include defeated knights as well as ladies, something that doesn't show up quite as much in Disney movies. Generally a true knight will show up and defeat the false knight and set all of his prisoners free.
But this sort of thing did not only happen in medieval romances, though that's definitely our main source for such stories. Consider also the Greek myth of Perseus and Andromeda, where Andromeda is chained to a rock as a sacrifice to a sea monster, but Perseus (technically a hero, not a knight) kills it and rescues her. This theme was repeated in Ariosto's Orlando Furioso, which is slightly post-medieval but very much in the tradition of medieval romances, with Roger rescuing Angelica from being sacrificed to a sea monster.
The damsel in distress story has ancient origins. A common plot device in medieval literature, it was also used in One Thousand and One Nights, believed to have been first collected in the 8th century C.E.
Even more ancient examples from Greek literature survive:
One famous example is Andromeda, whose mother offended Poseidon. Poseidon sent a beast to ravage the land, and Andromeda's parents fastened her to a rock in the sea to appease him. The hero Perseus slew the beast, saving Andromeda. Andromeda's plight, chained naked to a rock, became a favorite theme of later painters.
There's an old chivalric legend in Portugal called the Twelve of England about 12 knights that volunteered to fight 12 english knights that had each offended one english lady. You'll see it described in the Lusiads, the epic poem who touches on a lot of History.