2. Florence Nightingale
So the Doctor lands in the middle of a war zone: it's the 1850s, and he is faced with the Crimean War. While there, he meets "The Lady with the Lamp" herself, Florence Nightingale. She revolutionized the field of nursing, by being the first person to really say, "Hey, maybe all these people are dying because they're cramming into a dark room lying in their own filth. Maybe we should give them baths and wash their bed linens, and they might not die." Sounds like common sense, but given that this took place twenty years before Louis Pasteur and germ theory, her contributions were incredibly impressive. So tell me: is there any other person in the world that the Doctor would like to meet and have an adventure with? This woman, in an age where most women were just there to have respectable marriages and make babies, combined compassion and intellect to save lives. If done correctly, I could see her being one of those characters that you desperately wish could become a full-time companion.