Martha Louise Hudson
First episode: A Study in Pink
Seen also in: The Blind Banker, The Great Game, A Scandal in Belgravia, The Hounds of Baskerville, The Reichenbach Fall, The Empty Hearse, The Sign of Three, His Last Vow
Occupation: Landlady to 221B and 221C Baker Street
Show History: Mrs. Hudson is introduced as Sherlock and John's landlady when John first moves in with Sherlock; Sherlock is able to afford the flat, it seems, because he ensured Mrs. Hudson's husband would be executed for his crimes, namely murder. Although Mrs. Hudson is constantly reminding Sherlock and John that she's "not your housekeeper," she provides them with plentiful cups of tea and biscuits, and even manages to partially save John's date with Sarah in "The Blind Banker" by coming by with a tray of snacks. In "The Great Game," she also becomes crucial to solving the Connie Prince murder case, as her knowledge of celebrity gossip inadvertently reveals to Sherlock the cause of Prince's death (Botox).
In Season 2, Mrs. Hudson has become something of a mother figure for Sherlock; she has clearly entered into Sherlock's small circle of friends who he loves dearly. His fury when she is violently interrogated by CIA agents in "A Scandal in Belgravia" reveals just how much she has come to mean to him; the agent he throws out the window surely won't forget that any time soon. In "The Hounds of Baskerville," she is seen attempting to kindle a relationship with the butcher working downstairs, which Sherlock promptly squashes; in "The Reichenbach Fall," she is one of the three targets Moriarty chooses for his assassins, and thus one of the three people - besides John and Lestrade - that Sherlock cares about most and would sacrifice his life for.
In Season 3, Mrs. Hudson's back story is filled in a little more. "The Empty Hearse" shows her as still a member of Sherlock's circle of close friends when she is one of the people he chooses to visit when he "resurrects." In "The Sign of Three," she basically predicts the plot of "His Last Vow," as she tells John that her husband 1) cheated on her with many women, 2) ran a drug cartel, and 3) murdered a man by shooting him in the head, which are almost identical to when Sherlock 1) dates Janine, 2) takes drugs when he is undercover, and 3) kills Charles Augustus Magnussen in "His Last Vow." We also find out (thanks to Magnussen's files) Mrs. Hudson's full name (Martha Louise Hudson, maiden name Sissons), that she was an exotic dancer, and that she is apparently addicted to marijuana.
My take on her: Una Stubbs is flawless as Mrs. Hudson, and does a perfect job of balancing both the motherly and quirky sides of the character. Mrs. Hudson may come across at first as a bit scatterbrained, but she is nobody's fool, especially when she manages to hide Irene's phone for Sherlock in "Scandal" during the CIA agents' interrogation. Although her meandering chatter may have Sherlock putting her on "semi-permanent mute," she always has words of wisdom to offer him and John (or, as she likes to call them, her "boys"), and hilarious anecdotes about her own bizarre past. Personally, I hope Mrs. Hudson never leaves Baker Street; as Sherlock would say, "England would fall!"