Donna is my ultimate favorite thus far. She's got personality, she's witty and firey and stubborn, and reminds me of me (only I'm not quite so outgoing and "rawr!" very often, but just the way her thought-processes seem to work, I mean). Also she's still got that "new" feeling, in that she doesn't understand things yet. Probably would go out and cause a paradox if the Doctor left her alone too long, sort of thing, and I kind of like that she's not just instantly-ready for that sort of lifestyle, and is taking time to adjust to it. Also, redhead! <33
Honestly, I wasn't ever fond of Rose in the beginning. It wasn't until I was watching re-runs (sometime during season three, I went back and watched season two again) that I decided I actually did like her. Typically I have a thing against female leads, for some reason, and she was too much like the typical female lead character for me, then. But when I re-watched the episodes, I did grow to like her, making her my second-favorite companion - and the only one I would pair the Doctor with.
Martha is my least favorite, honestly. She just never had a real... story, personality, anything at all? She was just there to have an instant-crush on Ten, remind him of Rose sometimes, and push the season through. But somehow I think that season would have been more interesting if he'd been alone (or Donna had come in early?).
Which makes me sound terrible, but when compared to Rose and to Donna and even the Doctor, she just felt flat and forced. It wasn't the actress, it was the writing they did for her, and the way her arc was meant to be played. It just didn't work. I don't hate her, but it's bad enough I don't re-watch S3, whereas I definitely watch S2 and S4 episodes over again (sometimes even S1, but there I have issues with Nine, simply because I came into the fandom during S2 and therefore Nine is just strange for me. But that's getting off on another tangent).
When I Say Run - A Doctor Who Guild