Dorothea "Dodo" Chaplet came aboard the TARDIS during a particularly bleak time, after Steven and the Doctor fled from the massacre of the Huguenots in sixteenth-century France. She saw a little boy get hit by a car, and wandered into the ship looking for a policeman (this was back when people actually knew what a police box was). Steven came running back into the TARDIS warning the Doctor that policemen were approaching; fearing they would try and break in, the Doctor took off with Dodo still aboard.
Dodo was perfectly happy to be told that she was now on a possibly never-ending journey through time and space - she lived with her aunt, whom she said wouldn't miss her. Watching Dodo you get the feeling she also would have been perfectly happy to turn right around and go home and watch TV. Or get dumped on an alien planet and left there. Or have a burlap sack put over her head and asked to sit quietly on the floor. She wasn't very bright, is what I'm saying. But she was cheery and guileless and brought a much-needed touch of innocence to the TARDIS after the darkness of The Daleks' Master Plan and The Massacre.
And she maintained that cheery innocence even as she almost caused the extinction of the entire human race in her first full story, The Ark.
Here she is in a publicity shot from that story, in a non-existent scene in which she's happily carried away by a Monoid, one of the baddies of the piece. The TARDIS landed millions of years in the future on a great spaceship carrying the last of humanity to their new home as they fled from the destruction of Earth. This far in the future the common cold had died out, and humanity had lost all resistance to it. Sadly, Dodo had a killer case of the sniffles, and humanity's last hope started dropping like flies (along with future-boy Steven, who also had no resistance). The Doctor came up with a cure, but not soon enough - humanity was weakened, and when the TARDIS reappeared on the Ark seven hundred years later, humanity's former servants, the aforementioned Monoids, have enslaved the human race. Oh, that Dodo! You start to get mad at her for causing death on a massive scale and being responsible for the enslavement of humanity, but then you see that smile and you have to forgive her!
After putting this situation to rights the TARDIS trio moved on, and next encountered The Celestial Toymaker. This story was fun and frilly with very little substance - perfect for Dodo. Sadly, only the final episode remains, the others having been long-since destroyed by the short-sighted BBC. But here's the cast in that story - don't they look like they're having fun?
At the end of the story the trio are in fine spirits after having defeated the Toymaker, and Dodo offers the Doctor a piece of candy - which promptly cracks his tooth open. Oh, Dodo, is there anything you can't ruin? The TARDIS delivers its crew to Arizona in the old west in the next serial, The Gunfighters, so the Doctor can get some dental care from Doc Holliday. Steven and Dodo, meanwhile, dress up like Donny and Marie putting on an old-timey saloon sketch.
The Gunfighters is, quite frankly, a terrible story, but Dodo makes the most of it - the Doctor even acknowledges that she quickly lives up to "every cliché-ridden convention in the American west". She sings and dances in the saloon, she gets taken hostage...
...and she even gets to pack a six-shooter herself.
Granted, she looks like she has absolutely no idea what to do with the thing, but that's ok, this is Dodo. She's deadly without even trying.
Dodo says goodbye to Steven in her next serial, The Savages, and she and the Doctor travel on alone. They land on present-day (well, 1960s) Earth in The War Machines, and things are looking rosy. The Doctor is fond of Dodo - she reminds him of his granddaughter Susan, he once said - and she seems inordinately fond of him in return.
Unfortunately, fate - and the Doctor Who writers - aren't kind to poor Dodo. She's quickly mind-controlled by WOTAN, an evil super-computer, and brainwashed into trying to kill the Doctor.
Here she is being all evil or something. Halfway through the story WOTAN's hold on her is broken and she's whisked off to the country to recover, never to be seen again. At the end of the story we're told she's given her TARDIS key to her soon-to-be-replacement Polly, along with a message to the Doctor that she's decided to stay behind. And that's the last we hear of Dodo Chaplet.
Dodo gets a lot of grief from Doctor Who fans - she's a fairly generic, unmemorable companion as they go, with neither a proper introductory story nor even an on-screen departure. Nevertheless, I have a bit of a soft spot for her - yes, she's fairly lacking in characterization, and I still think either Katarina or Sara Kingdom would have made more interesting companions. But it's sort of charming how Dodo is relentlessly, almost aggressively cheery; she tends to wander blithely into the most dangerous of situations without a hint of concern or awareness. She sort of like the big dumb dog of the TARDIS crew - she makes a lot of messes but she's too lovable to stay mad at.
Unless, of course, you are a writer of officially licensed Doctor Who tie-in media, in which case you probably hate Dodo Chaplet with the intensity of a supernova. Yes, like all companions, Dodo makes a few appearances beyond what we see on the TV. Considering how innocuous her on-screen travels were, Dodo's spin-off adventures are comparatively...brutal.
In the novel The Man in the Velvet Mask Dodo falls in love with a Frenchman from an alternate timeline, sleeps with him, and contracts a disease in the doing - actually, microscopic engineered cyborg maggots. Yay. A cure is found, but she decides to keep the maggots as a souvenir of her first time. Yes, that's right, this was her first time. (Here's a quote from the TARDIS Data Bank, a sort of Wikipedia for Doctor Who - "She was also one of the few companions known to have lost her virginity whilst an active TARDIS traveller." Fun fact, kids!)
In Who Killed Kennedy?, we learn that WOTAN's mind-control triggered a psychotic break, and Dodo spent years in and out of psychiatric hospitals, convinced that her travels in the TARDIS were hallucinations. She wound up homeless, but found hope when she fell in love with a reporter. She became pregnant just in time to be murdered as part of a plot by the Master.
Oh, also, she once killed a guy who tried to rape her.
And the moral is, if you ever travel with the Doctor, do not grant licensing rights to novelists. They will take your innocence and piss all over it.