Doctor Who: Four
The Fourth Doctor: Tom Baker
First Serial: Robot
Last Serial: Logopolis
Costume: The TARDIS coat rack. Layers and layers of Victorian-Edwardian influenced twills and tweed, with as many pockets as possible, a hat worn shapeless and jammed onto his head, and a twenty-foot scarf of many colors. Add mad curly hair and a madder grin.
Companions: Sarah Jane Smith, Harry Sullivan, Leela, Romana I, Romana II, Adric, Nyssa of Traken
The Fourth Doctor is probably the one most remembered prior to the series revival. Particularly in the US, where a large portion of his run was shown on public television -- the closest thing we have to the non-commercial BBC -- his mop of curly hair, flapping coat, and insanely long scarf were most characteristically associated with the program by casual viewers. Clocking in at seven years on the show, Tom Baker was and is the longest continually-running Doctor, bested only by the one who technically held the title from 1987 through the cancellation of the classic series in 1989, to the TV movie in 1996.
Mainly what the Fourth Doctor was, was somewhat mad. Having just regained his freedom to travel in time and space, he continued to haul Sarah Jane Smith around the universe, accompanied briefly by the kindly but maddeningly traditional Harry Sullivan, a Naval surgeon who attempted to examine the Doctor just after his regeneration and accidentally ended up stowing away. (Ian Marter, the actor, was an active part of the DW fan community and wrote several of the series novelizations before he passed away of complications of diabetes in 1986.) Unfortunately, he found himself quite unable to rid himself of the pedantic people at home -- a persistent problem until the Time War, after which he rather wished he had them back. Dropping Sarah Jane off at what he thought was her home in Croydon (spoiler: It wasn't), he was yo-yo'd back to Gallifrey and saddled with both a quest and a keeper, a Time Lady named Romanadvoradrelundar. Romana for short.
Romana I was rather severe, but quickly decided it would be more fun to be his accomplice than his parole officer, and voluntarily regenerated into Romana II, played by the tiny, adorable Lalla Ward. The chemistry between the actors was so strong that they ended up married. The scripting for the show had regained the quirky tone for which it is most known today at this point, after having partially shed it between the Second and Third Doctors, owing in no small part to having the infamous Douglas Adams as a screenwriter and editor. He was responsible for "The Pirate Planet" (with Mary Tamm) and "City of Death" (with Lalla Ward), if you're curious; a third serial, "Shada", was left unfinished in perpetuity due to an ill-placed television workers strike, and a number of significant plot points from it were recycled for his novel Dirk Gently's Holistic Detective Agency. (There was a remount of sorts for BBC Radio decades later, using Paul McGann and Lalla Ward, and I can personally attest that it is hilarious.)
Unused location film from "Shada" was also used in "The Five Doctors" to explain the absence of the Fourth Doctor from the plot. Tom Baker was, somewhat understandably, heartily tired of the program when he finally left -- getting just as quickly divorced from Lalla Ward probably didn't help -- and for decades, declined to participate in any DW-related activities, preferring to go back to his other film and comedy work. Only in the past few years has he relented and begun associating himself with the program again, making a couple of series of audio adventures for Big Finish. Elisabeth Sladen is sadly no longer with us, but Mary Tamm, Lalla Ward, and Louise Jameson (Leela) have all participated, along with John Leeson, the voice of K9 as heard in both the classic series and the modern appearances of the little robot dog.
(Lalla Ward, notably, is also known for being an author and illustrator of children's books, and for being married to Richard Dawkins, whom she met at a birthday party for Douglas Adams.)
The Fourth Doctor is also notable for making it quite clear why he has a tendency to tow small women along on his adventures. Impulse control is not Sarah Jane's forte any more than it is the Doctor's, and Sladen is so tiny that the tall, gangly Baker developed something of a habit of simply picking her up and swinging her away from danger. Sladen in turn developed a habit of hanging on him when she wasn't punching peril in the snoot (and occasionally trying to throttle him when he was needling her on purpose). The relationship between the two characters is notably close even for a companion the Doctor was clinging to whilst running away from home yet again, and Tennant's affectionate, possessive delivery of the line, "My Sarah Jane," in "School Days" when they met again decades later was, if anything, something of an understatement.
Tom Baker is not unique in that he was essentially playing himself as the Doctor, but he was perhaps the one who altered his personality the least for the role, already being somewhat daffy and larger than life. If you hear him speak OOC, he sounds almost exactly like the Fourth Doctor, in fact -- most of his scripting is essentially someone writing down what Baker would have said had he personally been confronted with mysterious alien spaceships touching down in England.
The newly-regenerated Doctor attempts to leave Earth.
A stream of typically quick bafflegab from the Fourth Doctor -- he was prone to using rapid-fire pronominal referents to confuse the hell out of everyone who wasn't him.
A succession of crowning moments of hilarity from "City of Death"