Kate Stewart
Kate Stewart is an intriguing character, bridging the gap between Classic Who and the revival. Her father, Alistair Gordon Lethbridge-Stewart, had been a friend of the Doctor's and a leader within UNIT while the Doctor was stuck on Earth. After learning about her father's career, Kate joined UNIT, worked her way up to Chief Scientific Officer, and eventually became Commander-in-Chief.
Kate's first appearances in the revival were with the Eleventh Doctor, but she has now interacted with every iteration of the character since. This makes her uniquely widespread in her appearances, as most recurring characters only met one or two Doctors. In addition to showing up in Doctor Who home video adventures in 1995 and 2004, Kate has been in 13 traditional episodes from Series 7 through the most recent season and is slated to appear in the upcoming spin-off adventure The War Between the Land and the Sea.
Although it could be argued that she serves a plot function more than anything—revealing intel about threats, providing advanced weaponry, and connecting new companions with those in the past—Kate is a wonderful character when it comes to sparring with the Doctor. While they both respect one another and have good banter, Kate is ultimately a military leader. She readily fights with the Doctor when his tendency for mercy puts humanity in danger and has proven herself willing to take more drastic, cruel actions than he will.
Because Kate appears in so many different seasons (and under many different writers), her characterization can be inconsistent. While she cut the "Lethbridge" part of her name in the Moffat era to avoid nepotism, for example, she claims it during Davies's second run. Her commitment to her father's "science leads" philosophy also wavers in different episodes.