A recurring joke about the Daleks is their inability to go up stairs. Two Classic serials ("The Chase" in 1964 and "Destiny of the Daleks" in 1979) have characters pointing this weakness out — in the latter case, it's key to the Doctor's plan to escape! This weakness was addressed in the 1988 serial "Remembrance of the Daleks", but the jokes persisted at least up until 2005 when "Dalek" — which also addressed this point — was shown. It's perhaps worth pointing out that, by the time the first story aired, the audience of Doctor Who was roughly three guys and a dog, so it's possible that not enough people actually saw it for the change to sink in.
It was addressed before then — one earlier episode showed them to have somehow gotten up a staircase without it actually being shown on screen.
And in some quarters it's still what the Daleks are most famous for, despite the fact that the Daleks, in at least the Russell T Davies era, spend half their time flying around like nobody's business. (A large portion of the Daleks' appearances in the Steven Moffat era have been inside the Dalek Asylum and on board a Dalek spaceship, though hovering Daleks still make appearances.)
There's a very common assumption, even among fans, that the companion was until recently a screaming ineffectual Damsel in Distress. In actuality, from the first series there have been plenty of male companions. Even the female companions actually screamed less then the modern ones, with plenty of characters like Leela, Sarah Jane and Ace who went well against the trope
The Doctor, especially the Third, is often referenced by his supposed catchphrase: "Reverse the polarity of the neutron flow!" Which the Third Doctor said exactly two times, eleven years apart, as well as once more in a play. The Fourth and a clone of the Eleventh (going through other phrases of his incarnations) used it once and the Fifth and the Tenth twice.
He did say "reverse the polarity" a few times during his initial run, though. Just not the full phrase.
A lot of traits associated with the Doctor's character in general are actually just traits of the more popular incarnations, usually the Fourth or Tenth — a sort of vague conglomerate Shallow Parody Doctor who wears Victorian clothing and a long scarf, eats jelly babies, is always comically dramatic about everything, suffers great and dramatic internal conflict over all the genocide he has to do, kisses teenagers and cries about it, and won't touch a gun. Gareth Roberts (a writer on the New series) pointed out in an interview that there's an idea that the Doctor talks in Antiquated Linguistics, something only vaguely touched upon by the Fourth and Sixth, and even then only in moments.
The Fourth Doctor actually wasn't as big on the jelly babies as people remember — at least until the Graham Williams era kicked off. He offers some to Sarah and Harry at the end of "Robot" and tosses the bag to Vira at the end of "The Ark in Space", and a second bag appears amongst various Cow Tools when turning out his pockets in "Genesis of the Daleks" (in a scene that's really easy to miss). That's it for the whole of Season 12. They don't appear at all in Season 13. In fact, the Doctor uses his yo-yo gimmick more frequently than the jelly babies in the Hinchcliffe era (making nine appearances versus the jelly babies' six appearances). Somehow, simply because it was featured early on, the jelly baby association stuck enough that featuring more jelly baby scenes in Season 14 was catering to fan demand (see the letter to Robert Holmes featured on the DVD of "The Brain of Morbius" in which a fan asks what happened to the Doctor's jelly babies). It's not until Season 15 that the "Hello, I'm the Doctor, would you like a jelly baby?" routine begins to show up, and even then it's still absent more often than it's used.
The many fans who consider Adric The Scrappy will never, ever, stop talking about the moment in "Four To Doomsday" where the villain Monarch convinces him to support technocratic dictatorship in about three minutes of conversation. This has been blown up into Flanderisation of him "always siding with the villain", even though the only other times it might be claimed to have happened were two obvious attempts to become a mole and one when it was very clearly against his will.
The Sixth Doctor trying to choke his companion Peri to death after a dodgy regeneration. It's still what many fans remember him for.
The fact that the Eighth Doctor was the first Doctor to openly snog his companion is enough that he is strongly associated with snogging in the fandom memory and serves as a target for all the joy and horror that implies, even though his successors the Tenth and Eleventh Doctors did more snogging than he did. Each. This reputation was arguably deserved at the time the movie came out, but even after the Ninth Doctor confirmed himself to enjoy sex and snogged a bloke, the Tenth Doctor won awards for an episode about him seducing and shagging a courtesan, the Eleventh Doctor had a whole Arc about his marriage and consummation of it with a female character, and the Twelfth Doctor set up a hotel-restaurant via Tricked Out Time solely so that he could spend twenty-four years banging his wife there, the Eighth Doctor is still stereotyped as the sex-maniac.
The Doctor from the ninth onward in general. With the original series' No Hugging, No Kissing rule being relaxed in the new series, any sign of him not being completely asexual is treated as him having become a sex maniac to rival Jack Harkness. In fact, he gets kissed, to his hilariousbewilderment, as a Running Gag and so does a lot of snogging whether he wants to or not, and has had flirtatious teasing with several characters, and that is quite a change from the classic series, but that's light-years away from "every companion is also a love interest, and he's banging every Recurring Character on the side." In fact, a theme that's also played up more in the revived series is how ancient and alien and alone the "lonely god" is, making the normal idea of a romance with him impossible (as several characters who have loved him have learned. River Song would give anything for their arc to be about "consummating" anything. Though yes, technically she is his wife. As always with the Doctor, it's complicated). Shipping Goggles combine in a very nasty way with the fandom's defensiveness of his asexuality: In most shows, to fans, the two leads being close means they're shagging. In Doctor Who, the two leads being close means they're shagging — and therefore the Doctor and the series are ruined.
From the other direction when it comes to the Doctor's asexuality: The idea that he's completely asexual and aromantic mostly derives from the Fourth Doctor's line to Countess Scarlioni in "City of Death", "You're a beautiful woman, probably." Since the First Doctor's first companion had been his own granddaughter, chances are that line wasn't intended to say romance is 100% foreign to him — and Tom Baker's delivery of the line leaves open the interpretation that he's conveying to her that he's aware that she's trying to use her attractiveness to distract him. (Supporting this is that the line takes place while the two are drinking together, and follows some UST-laden interactions between them such as the Countess and Count discussing how the 'tall man' must have found her attractive, and the Doctor collapsing into her lap.)
The Eighth Doctor in Expanded Universe works is always losing his memory because it's a memorable (heh) thing that happened in the movie that is his only TV appearance. Thing is, the Doctor is alwaysout of sorts for a while after regenerating, and what we got in the movie is typical for that period. There's no reason to assume Eight would be particularly susceptible to memory loss, it's just that it was a big part of his only onscreen appearance.
The Ninth Doctor called humans 'stupid apes' once, but it's become something very strongly associated with his character — not just in fanfiction, where he drops 'ape' at least once a fic, but Christopher Eccleston even did it himself while briefly reprising his role (!) in a guest video for the BFI's Doctor Who 50th Anniversary party:
...I, the Ninth Doctor, vow to save the universe and all you apes in it.
Rose Tyler eats lots of chips. She doesn't: they're mentioned in her first two episodes, then she eats some in her first finale and "School Reunion". But fans are convinced.
A good part of the fandom remembers Martha Jones only for her unrequited crush on the Doctor, despite having more personality than that and actually getting over it at the end of her season.
In "The Shakespeare Code", when the Doctor and Martha are confused about what is going on, the former makes the odd statement that Rose would know what to do or at least say something to inspire a realisation, to Martha's understandable annoyance. The Tenth Doctor never brings up Rose again to Martha yet he's often remembered as spending the entire third season mourning her and gushing about how much better than Martha she was.
When Donna Noble first appeared in "The Runaway Bride", she slapped the Doctor twice (once because she thought she'd been drugged and kidnapped, another time because he was being rather deriding of that). Since then, she's never slapped him again and went through a lot of Character Development to become the Doctor's moral compass. Her main characteristic in fanfiction is slapping everyone. Well, that and her memory loss. That particular plot point created the 'Donna Fix-It' fic.
The Tenth Doctor's last words; "I don't want to go." A Tear Jerker for some but Narm for others.
It didn't help that this was preceded by Ten being completely horrified of his impending death, acting like he would really die and the next Doctor would be someone entirely different, something none of the previous Doctors did.
Or that he ended his appearance in the 50th Anniversary special by saying it again, for no real in-universe reason.note The out-of-universe reason likely being to head off fan arguments about what should count as his "real" final words. And then Eleven actually tells Clara "He always says that."
The Eleventh Doctor only had one main episode where he wore a fez hat, but since then, almost every drawing of him includes him wearing it. (There were a couple of later Continuity Nod moments where he wore a fez for about two seconds each.) This even led to a Brick Joke when a fez he talked about ordering finally arrives two regenerations and somewhere between hundreds to billions of years later. It even shows up on the showcase art for 11's Magic: The Gathering card!
Amy Pond forcibly kissed the Doctor, and tried to seduce him, at the end of "Flesh and Stone". Even though she never does it again and remains faithful to her fiancé then husband Rory for the rest of her run, some fans still resent her for this. Steven Moffat quickly came to regret writing the scene and especially playing it for laughs.
Rory has been referred to in-show as "the man who dies and dies again." He's only done it for real once. He's just...very good at creating the illusion of death. By accident. Lots. It's also strange that Rory alone is remembered for this — Steven Moffat has a habit of having everyone die a lot.
bewilderment,