Over the course of watching through the surviving Classic Doctor Who stories in order with
EvilBen and
ophiomancer (we're currently about half-way through the Troughton (Second Doctor) era), it's occurred to us that just about all of the Doctor's companions fit the archetypes of the original three companions from the beginning of the show.
Ian was the original Handsome Male Lead of the series, usually filling the Action Hero role. Ians are characterized by being action-oriented and street-smart and having a sense of responsibility independent of the Doctor's, providing both muscle for action-heavy stories and a push for the rest of the party to adopt more direct, confrontational plans, and often taking a leadership role independently of or in support of the Doctor.
Barbara was the secondary hero of the early series, taking a knowledge-based hero role to complement Ian's action-hero role. Originally, they'd switch off the lead, with Ian being the primary hero in sci-fi stories and Barbara in historicals. Barbaras are characterized by being calm, collected, and resourceful, contributing the the party with practical knowledge or technical skills, and often acting as the party's moral compass in terms of thinking through the far-reaching consequences of their actions.
Susan was the Doctor's 15-year-old (or the Time Lord equivalent thereof) granddaughter, placed in the series to act both as a mysterious figure (adding depth to the mysteries around the Doctor's background) and as a sympathetic audience surrogate -- a difficult balancing act to pull off, and one that met with only limited success with the original Susan. Susans are characterized by innocence and naivety, often combined with a very high level of raw intelligence and book learning, and almost always combined with being curious to a fault. Their plot role is the classic "chick" role: heart and soul of the team, sympathetic audience surrogate, and driving the plot by wandering into trouble and needing to get rescued. But for most Susans, the raw cleverness shows through enough to give the character flashes of awesomeness.
In thinking through categorizing the companions, there are some that only sort-of fit in the original framework, with the big problem being that some of the buckets (especially the Susans, and to a lesser degree the Ians) seem a little too big: for example, Zoe and Romana fit best as Susans, and Dodo and Rose fit best as Susans, but the former two are very, very different from the latter two. This is resolvable, though, by subdividing the Susans into three categories: Zoe-Susans (who emphasize the intelligence and cleverness), Vicki-Susans (who emphasize innocence, naivety and "heart"), and Mixed Susans (who balance the characteristics). Likewise Ians can be subdivided into Brigadier-Ians (who emphasize initiative, responsibility, and leadership), Jamie-Ians (who emphasize strength, combat skill, and street smarts), and Mixed Ians.
So, my classification of the Doctor's companions over the years:
Hartnell Era
Susan Foreman -- Mixed Susan
Barbara Wright -- Barbara
Ian Chesterton -- Mixed Ian
Vicki -- Vicki-Susan
Stephen Taylor -- Jamie-Ian
Katerina -- Vicki-Susan
Sara Kingdom -- Mixed Ian
Dodo Chaplet -- Vicki-Susan
Polly -- Barbara
Ben Jackson -- Jamie-Ian
Troughton Era
Jamie McCrimmon -- Jamie-Ian
Victoria Waterfield -- Vicki-Susan
Brigadier Alistair Gordon Lethbrdige Stewart -- Brigadier-Ian
Zoe Hariot -- Zoe-Susan
Pertwee Era
Liz Shaw -- Barbara
Captain Mike Yates -- Mixed Ian
Jo Grant -- Vicki-Susan
Sergeant Benton -- Jamie-Ian
Sarah Jane Smith -- Mixed Susan
Tom Baker Era
Harry Sullivan -- Barbara? (or maybe Mixed Susan?)
Leela -- Jamie-Ian
K-9 -- Doesn't fit the categorization
Romana -- Zoe-Susan
Adric -- Mixed Susan
Nyssa -- Don't remember her well enough to categorize
Tegan Jovanka -- Don't remember
Davison Era
Vislor Turlough -- Don't remember
Kamelion -- Don't remember
Peri Brown -- Vicki-Susan
Colin Baker Era
Melanie Bush -- Don't remember
McCoy Era
Ace -- Mixed Ian? (or maybe Jamie-Ian)
McGann Era
Grace Holloway -- Mixed Susan
Eccleston Era
Rose Tyler -- Vicki-Susan
Mickie Smith -- Vicki-Susan
Captain Jack Harkness -- Jamie-Ian
Tennant Era
Donna Noble -- Barbara
Martha Jones -- Barbara
Wilfred Mott -- Not sure
River Song -- Brigadier-Ian
Smith Era
Amy Pond -- Mixed Ian
Rory Williams -- Barbara