Until 2007, when I discovered the weird and wonderful world of online Doctor Who fandom, my answer to the question of "who's your favorite companion" was straightforward. Liz Shaw, played by the late Caroline John.
Why did I leave her behind? Simple: there's no skin in the game where Liz Shaw is concerned. She's uncontroversially, incontrovertibly, awesome. She's the only Who companion fired because audiences didn't like that she was smarter than the Doctor.
One has to wonder whether the discomfort lay not only in the idea that a human could equal the Doctor, but a human woman at that. After all, when she left, the writers gave us Jo Grant, the archetype of googley-eyed alien father-figure worship. Liz had no time for hero worship; she was too busy getting shit done.
The writers certainly knew this. Think of Inferno, which depicted a parallel Earth where the Brigadier and UNIT's military arrogance had gone almost completely unchecked, save for the restraining influence of Liz's alter-ego. The Doctor knows she's the only one who can be reasoned with in any Earthbound scenario; again and again, she proves him right.
Her time on the show was all too short, but there's no other companion who had such a strangely perfect run of episodes. Spearhead from Space offered terror rarely seen until the Moffat episodes of Nu-Who, while Ambassadors of Death perfectly captured both the uncertainty and excitement that accompanied our real-life forays into outer space. Then there was The Silurians, certainly one of the finest explorations of humanity in the show's history.
These stories were dark, reflective of science fiction themes the show hadn't really addressed before, and hasn't since. This couldn't have happened without giving the Doctor a human equal, someone to show that the dangers are real, not just fictions in the mind of a judgmental alien with a god complex.
Liz Shaw was that equal. Caroline John may have passed, but her character lives on as one of the greats.