I find it interesting how I share favourite or well-liked Doctors with some of the previous posters but totally diagree on others. I haven't yet seen everything of the old show. I'm currently working my way through it in broadcast order and am now in season 15, in the middle of Tom Baker's tenure, so I can't rank all the Doctors. Additionally, I find it quite hard to actually rank them so it'll be more tier-like and free form.
My two favourite Doctors are David Tennant and Jon Pertwee.
10 will probably always be 'my Doctor', even though I started with 9. He was very diffferent from his predecessor, even more manic but also mellower despite his claim of "No second chances. That's the kind of man I am." I know some people dislike Tennant's acting style but I love it and I can't help grinning when his Doctor does it or gets all positively excited about something. There were also some dark aspects to him, even in his first story, which I find interesting and fascinating. I also liked the tragical elements of his life and backstory (e.g. the loss of the Timelords, his unfulfilled love for Rose).
As for 3, well, others in this thread have already sung his praises. I admire his style, his charms, his witty and sarcastic remarks and his anarchist streak. My fascination with him is also due to his multi-layered character. Many things have been written about the infamous shower scene in Spearhead from Space
, I'm sure, but it really impressed me and stuck with me because we get to see this bad-ass tattoo. To me, that made it immediately clear that this guy with the frilly shirts and the velvet dinner jackets is actually a bad-ass if he has to be. Another aspect I really love about this Doctor is his frustration about his exile and the fact that he would abandon earth and UNIT in a heartbeat if he got his time travel capabilities back early on in his tenure. Apparently, I like my characters a bit flawed. The interactions between him and the Brig and the Master are great, too. So, while some of his stories are kind of weak and/or silly, it's always a pleasure to watch him and his interactions with those people.
I find it hard to rank the following four Doctors, really, also because I feel I need to do some rewatching, especially in regards to the Hartnell era which I don't remember too well anymore. So bear in mind that the differences between them is marginal and that it could change.
I fully expected to dislike Tom Baker because he followed Jon Pertwee whom I like so much but he had me on his side after the first few minutes in the role. He's especially crazy and confused in Robot
but I loved it. I also admire how he does all the running around, climbing and other stuff without tripping over his scarf.
There's, of course, more to him than just the craziness - I love how he can change from crazy to speaking with authority within seconds and that it's actually convincing. One thing I also like about him is that he seems to be more fallible and vulnerable than his predecessors and has to be saved by his companions in some way pretty often. Since I haven't yet seen everything of his tenure I can't comment on his later years which have been criticised in this thread.
Christopher Eccleston was my first Doctor. He was the Doctor when I fell in love with this weird little show (towards the end of The End of the World
). His Doctor was a mix of madness, anger, hope, despair, passion and kindheartedness and I really like that. While I enjoy other Doctors a bit more I'll always remember him fondly. The scene I associate most with him is his final one when he addresses Rose and says, "You were fantastic. And you know what? So was I." because it's true.
I really can't decide between Patrick Troughton and William Hartnell. At the moment, I slightly favour Troughton because he played the character in a comedic way but still managed to convey depth. I appreciate how the Second Doctor doesn't seem to know what he's doing half of the time but actually knows it pretty well.
I was very impressed by Hartnell when I started watching the serials of his era. And there are some pretty great ones. I liked his grumpyness, how he addresses Ian as "dear boy" and ends many of his sentences with a "mmh?". I think that Hartnell did a good job of conveying the alienness of the character, especially early on. He suffers a bit from a streak of mediocre and dull stories later, towards the end of his tenure.
At the moment, my least favourite Doctor is the current one. I can't really connect to him and find him just a bit too weird and also strangely disconnected. However, this may be down entirely to me not being able to get into Moffat era Who because I did like him a lot when he showed up in The Sarah Jane Adventures
. His tenure isn't over, yet, and the new direction they seem to take him - judging from the last Christmas special - has piqued my interest.