For me, it's the theory that in the original Spider-Man trilogy, Aunt May knows about Peter's secret identity.

I don't know whether the theory has been confirmed or dismissed, but there are quite a few rather obvious hints:

• one scene in the second movie when Spider-Man rescues Aunt May from Doc Ock and he says to her: "We sure showed him." She replies "What do you mean we?" and looks somewhat suspicious and moves her head slightly in an over the shoulder shot, indicating that she may be pondering about Spider-Man's identity after possibly recognizing her nephew's voice. Before that, she was hanging from a building and Spider-Man screams to her to hang on, after which she gives him another uneasy, suspecting look.
• Aunt May's motivational speech later in the same movie in which she states in a very implicative tone that kids like Henry need a figure like Spider-Man to look up to, suggesting that Peter has to continue being the hero he's meant to be. The way she looks at Peter during her speech further indicates that she's subtly encouraging him to keep being Spider-Man. He's about to give up because of all the misfortune he's been having, but she emphasizes her words yet again when she says to "hold on a second longer"; on a rewatch, I noticed that's also when Peter looks up to her as if he realizes that she's speaking directly to him and knows of his struggles. For me, that sentence is the one that convinced me: Peter, the hero, taught Aunt May to hold on when she was at the verge of falling to her death, and now she's repeating his exact words to him.

I like that it's not definitively mentioned in the movies, because it makes for a really interesting debate. I can totally see it being a complete coincidence and that she only cares about Peter and encourages him to be a good person – a hero, as she puts it –, which doesn't have anything to do with being a superhero. So in the end, whether Peter is Spider-Man or not doesn't matter to her. And that in effect means that whether or not she knows shouldn't matter to us.