For me it's hard to choose as there isn't much room between a lot of them. I think you have to look at it two ways... how well did the actor perform the part written for them, and how was the character written.
For instance, I agree with some of what others have said with Martha, the fact she had a crush on the Doctor lessened her character a great deal in my eyes, and that is probably one of the reasons Donna was so popular because she was more of a traditional companion and not all "gooey eyed". If Martha had not had a thing for the Doctor then I'd imagine she would be a lot more popular. I think Freema was a good actress and played the part well.
So my list goes
Donna
Rory
Amy
River
Wilf
Rose
Jack
Martha
For instance, I agree with some of what others have said with Martha, the fact she had a crush on the Doctor lessened her character a great deal in my eyes, and that is probably one of the reasons Donna was so popular because she was more of a traditional companion and not all "gooey eyed". If Martha had not had a thing for the Doctor then I'd imagine she would be a lot more popular. I think Freema was a good actress and played the part well.
So my list goes
Donna
Rory
Amy
River
Wilf
Rose
Jack
Martha