There has been many directors through out Doctor Who history, of course. I've many ones that I really like. It is kind of funny, when I think back just 10 years ago, I wouldn't even know any director for anything, but then I got interested into how the shows/movies were made, and started to pay attention.
My favorite director will have to be Richard Clark. He has directed four episodes in the show. . He directed two Series 3 episodes; "Gridlock" and "The Lazarus Experiment". He also directed two episodes of Series 6 "The Doctor's Wife" and "Night Terrors" I really liked the feel and look of all these episodes.
That is it for now, sorry it is short, I might add to it later.