4. Amelia Earhart
How has there not already been an episode with Amelia Earhart? Amelia Earhart was pretty much one of the most famous pilots in history, being the first woman to fly solo across the Atlantic Ocean. In 1937, she attempted to circumnavigate the globe, but she vanished under mysterious circumstances, never to be seen again. Which, let's face it, just has the Doctor written all over it. Picture this: they meet Amelia, she goes on her legendary flight, but she never actually crashes. If I was writing the story, I would have it go this way: she has an adventure with the Doctor and ends up on another planet or something, where she decides to stay. Or maybe even dies there, which would certainly be a bold move, but might be a bit morbid for the show as it currently stands. There would be the same old conflict about whether or not the Doctor can change established history, until he realizes that he was always meant to take Amelia with him. That's why no one ever found any remains from her body or plane. It's a perfect opportunity to play with a popular historical figure that has enough leeway that you don't feel like you just totally changed their life story.