1. A Conflicted Time Lord
This is a weirdly specific premise, but hear me out, I think it's a good one. The Ninth Doctor famously said, as he was about to regenerate, "I could have two heads. Or no head!" Now, I've never seen a Time Lord absent of any limb whatsoever, or looking at all different from a human being. Nor would I especially like to. It's just really to reinforce the idea that, through regeneration, the Doctor can become anyone. This is a fantastic premise, but one I don't think the show has really taken advantage of fully. Imagine this, if you will; the Doctor regenerates, and doesn't want to save the universe. He has no special penchant for heroics, or for saving innocents. He's a coward, essentially. Now, I know what you're thinking, that doesn't sound like it would make a very good TV show. Indeed not, but it would enable the Doctor to re-discover, through his companions or his situation, who he truly is. The Doctor is a hero, that is the essence of the man. But I would relish the chance to see him forget that, for a moment, only to re-discover it through his passion for the universe and for life, and for the audience to rediscover it along with him. For one thing, it would be a great access point for new viewers, and a magnificent way to refresh the show. I admit it's a weird premise, but it's one I'd love to see nonetheless.