Well, what does the word "definitive" mean, exactly? It doesn't just mean the best or favorite or most important one, but the one that most
defines that Doctor or that era, that is the authoritative statement about who and what that Doctor was.
So for the First Doctor, I'd say the Ian/Barbara pair, because what defined the First Doctor was that he was more of a mentor figure for the young male and female characters who were the actual leads as the show was originally conceived.
For the Second, I can see Jamie being considered definitive because the Second Doctor was almost never without him, though I'm not sure what kind of statement Jamie actually makes about that Doctor or his era, aside from the fact that he still needed a young, tough male lead to do the running and punching. I think that in a way, Victoria could be considered definitive in that she embodies the Troughton era's focus on scary monsters and the sense of vulnerability the Doctor and his companions had. (If we were talking favorites, though, it would be Zoe, Zoe, Zoe!)
For the Third,
io9's obituary of Caroline John made a good argument that Liz Shaw played a key role in redefining
Doctor Who for the '70s as a more serious and more down-to-Earth show, despite her short tenure. Other than that, as much as I adore and cherish Jo Grant, I'd say the definitive "companion" of the Pertwee Era was UNIT.
For the Fourth, it's probably Sarah Jane, since she was the archetype for the stronger, more equal female companions who emerged in that era. Though for the Graham Williams-produced seasons where the show got goofier, I'd say the definitive companion, the one that most embodies the era, was K-9.
For the Fifth, no one companion can be definitive, since it was the larger group, the family dynamic, that defined that era. If I had to single one out, it would be Adric, because he embodied the role of the companion in that era as someone who had a knack for getting into trouble and thereby made the Doctor more vulnerable. And his death is surely one of the definitive moments of that era.
For the Sixth, I suppose Peri is the choice by default, though one could make a case for Mel as the symbol of the era, in that she was lightweight and never had her potential fully realized, but at least was lively and colorful. (I'm not familiar enough with the books and audios to nominate anyone else.)
For the Seventh, it's naturally Ace, representing the darker turn the series took, the more nuanced characterizations, and the new role of the companion as a pawn of the Doctor.
For the Eighth, you'd have to go to the audios or books, so again I'm not really qualified to say.
For Nine, it's Rose by default, and it's probably her for Ten as well; arguably she was the definitive companion of the Russell T. Davies era.
And for Eleven it's Amy by default, so far. Rory and River are important too, but they're both defined largely in relationship to Amy Pond, who's pretty much the central axis of the entire Moffat era so far. At times, it has seemed more like the Doctor was Amy's companion.