3. Nyssa of Traken
Nyssa was the daughter of Tremas, a nobleman of Traken who met the rather unfortunate fate of becoming possessed by the Master. Traken itself was also the victim of one of the Master's many nefarious schemes. Having been led back to the Doctor by a projection of his future regeneration (difficult to explain, just watch Logopolis), Nyssa decided to stay aboard the TARDIS after Traken was destroyed. Being thoroughly educated in the sciences enabled Nyssa to understand the Doctor's world to a greater extent than some of his previous companions had, and the Doctor, in turn, appreciated having a companion who was more or less able to understand him when he spoke. He so respected her knowledge and expertise that he allowed her to assist him in flying the TARDIS, a privilege very few companions ever enjoyed. In many ways Nyssa was a second Romana, a companion who was almost an equal. Nyssa's departure was precipitated by her catching the often-fatal Lazar's Disease after the TARDIS landed on a hospital ship. Granted, the hospital managed to cure her, but she recognized that their methods were unstable, and the cure itself had a reputation for sometimes kill the patients it was supposed to help. Nyssa knew the hospital ship would benefit from her scientific knowledge, so she chose to leave the TARDIS and help her fellow sufferers. This parting was bittersweet--the Doctor was sad to lose Nyssa, yet at the same time he was proud of her for deciding to dedicate her life to others. I think it would be fitting for him to find Nyssa again to see what she has accomplished. Also, he and Nyssa have something in common now--they are both the last of their kind. This, I think, would make for an interesting new dynamic between them.