I guess it depend which Doctor. They change after each regeneration so they don't necessarily have the same feelings toward a companion.
I think 9 & 10 loved Rose and 11 Amy.
May be 11 is gonna really fall for River latter on (hopefully not though) but right now, I really thinks he love Amy more (in a totally non romantic and platonic way).
I think if you talk about the whole of Doctor Who, (including the classic series) I think it would be Sarah Jane. He called her his best friend. I guess it all depends on the personality of the current Doctor. Right now, I would say River, since they are married.
I disagree with the first respondee. I think that they do have different feelings, (i.e., "You were the first face this face saw" scene with Amy) however I believe the doctor withstands the same conscious memories of each companion. Sarah Jane, Rose Tyler, and Amy Pond, in my personal opinion, hold the most special places within the Doctor's hearts.
