Doctor Who is an example of Alternate Character Interpretation within a series, thanks to being portrayed by thirteen different actors (in canon, anyway) and a slew of writers, directors and producers over half a century, the Doctor has received every interpretation imaginable, from eccentric wanderer, to a literal god, and everything in-between. Not to mention the various speculations on the nature of the Doctor's relationship with various companions.
Apropos "Night of the Doctor", SF Debris floated a theory about regeneration trauma on his site's blog. Time Lords are meant to regenerate on their home soil of Gallifrey. The TARDIS, while equipped for emergency regenerations, is a poor substitute.
With Ten in particular, the question is, "Does he mean well?" Many are convinced he's being intentionally written as an egotistical Jerkass who demands the attention of others and refuses to give anything in return, running roughshod over people's lives and never feeling the need to explain himself or ask permission.
Ten's regeneration scene: one of the most moving and emotional scenes in the franchise's history as he desperately hangs on for as long as possible, or an act of spite against his next incarnation, forcing him to be born in a crashing TARDIS? Or both?
Perhaps the Tenth Doctor's strident pacifism is a form of detached arrogance fitting with his god-complex. He pompously berates the "little" lifeforms for using violence (frequently in self-defence) because, as a Time Lord, he has no way of seeing things from their perspective or at their level (or at least no way that sticks after he reopens the fob watch). There's a hint supporting this theory in the episode "The Christmas Invasion" from 2005: Ten berates the Prime Minister for destroying a Sycorax ship. The Prime Minister measuredly responds by telling him that Earth needs to defend itself because the Doctor is "not always [there]". Ten petulantly rejects this and sets events in motion to force the Prime Minister from office.
Which in turn results in disaster for the UK (and indeed, the entire Earth) for years to come, as first the Master and then the Children of Earth government succeed her. Apparently by Eleven's time, It Got Better.
And despite his pompous attitude, Ten is not the pacifist he sometimes claims to be. He can get quite nasty. Either by losing his temper or worse, while telling you how sorry he is.
Rose Tyler. A book dumb but brilliant girl who was loving and caring, and helped the Doctor recover from the pain of his war, but with human flaws? Or a Bitch in Sheep's Clothing who cares nothing about her friends and family, cannot take responsibility and is unable to cope without the Doctor? Or a mix of both?
A lot of the criticisms that Amy faces can be said the same for Rose, but RTD fans seem to overlook because Rose was their first companion.
The fact that it seems Rose gets whatever she wants annoys fans. Create a paradox and almost destroy the universe? Get a second chance, despite the episode before, the Doctor kicked someone off the Tardis for trying to do that. Lose your dad? Get him back but this time, he's rich. Trapped in a different dimension away from your boyfriend? Have your rich father create a device that allows you to dimension hop. Can't be with the man you love? Hook up with his clone. This video from Welshy really illustrates this view.
Is the Eleventh Doctor more like an old man with a child's personality and a young man's body, or a child with an old man's wisdom and memories and a young man's body? And for that matter, how much of his eccentric, playful demeanor and silly mannerisms is a pasted-on Stepford Smiler coping mechanism and how much is just his natural state?
In-Universe, the Eleventh Doctor episode "The Pandorica Opens" gives us an idea of how the Doctor is seen by species he doesn't save every week - particularly the Always Chaotic Evil ones, but possibly also the no-worse-than-humans ones as well: he's a world-ending demon who must be shut away for all eternity before he destroys the entire universe.
There was a goblin. Or a Trickster. Or a warrior. A nameless, terrible thing, soaked in the blood of a billion galaxies. The most feared being in all the cosmos. And nothing could stop it, or hold it, or reason with it. One day it would just drop out of the sky and tear down your world.
You make them so afraid. When you began all those years ago sailing off to see the universe... did you ever think you’d become this? The man who can turn an army around at the mention of his name! Doctor. The word for healer and wise man throughout the universe. We get that word from you, you know. But if you carry on the way you are, what might that word come to mean? To the people of the Gamma Forests, the word "doctor" means "mighty warrior". How far you've come!
It should be noted that when those species come to confront him, it's right after a frantic monologue wherein he's literally shouting at the sky like a madman, daring entire armies of his enemies to come get him, and implicitly saying that he can take them all by himself. In a later episode, he has another monologue instructing a man to humiliate himself as an example to future aggressors. This is after The Doctor's enemies had already agreed to surrender. The Doctor, Eleven in particular, is often a vicious, brutal enemy.
Some of it's the writers trying to force it where it doesn't really go - most of the time, when the Doctor is confronted thusly, he's done nothing wrong. But nobody ever blinks an eye at any of the worst of the Harriet Jones-type moments. The Tenth Doctor era was plagued by it, but far from the only time this has appeared. A guy who can bring down Daleks, Cybermen, and other planet or even universe-threatening foes is kinda scary, but that doesn't mean he's wrong for doing it. It looked like we were headed back there, but we finally get some elaboration of those who fear the Eleventh Doctor so much: they think the future destruction of the universe that's causing the Timey-Wimey Ball its present distress will be his fault. In the season finale, when the Doctor is about to have to make a Heroic Sacrifice, River Song can't let him go without showing him how much the whole universe loves him and would have done anything to save him if they could. He's also more likely to be questioned when actually going too far, or not seeing the full effects of what he's doing.
Let's look back in a Town Called Mercy,the Doctor thinks that since he's the Last of the Time Lords that's he's the only one who can defend time and space now; that he and that he may as well have pulled the trigger on everyone ever hurt by those he didn't take down. That mindset is completely justified. He has showed mercy to villains like the Master and Davros a lot of times in past, allowing them to live despite their horrible actions. This act, however, has gotten many, many more people killed whose deaths were caused by said villains later on. How can anyone honestly blame the Doctor for acting that way since that is just one example that his mercy has come back to bite him on the ass?
On the companion side of things, Amy Pond has been getting a lot of this. Is she a quirky girl/young woman who never quite fit in and has found someone like her in the Doctor? Or a somewhat unbalanced, obsessive woman who can't relate to anybody easily because she's just spent that long devoting her life to waiting for the Doctor? How much of this is directly because of her abandonment by the Doctor, and how much is just her?
And then there's the issue of how she had a psychic parasite living in her house and actively absorbing her memories from her formative years through to adulthood...
On top of that, the crack kept pouring the Universe through her dreams. The Doctor says that affected her memory; did it affect anything else?
And now she remembers all sorts of complicated events that never really happened; what would that do to your mind?
She can also been seen as having an attachment disorder.
This carries on another of Eleven's major companions, River Song. Is she an egotistical psychopath who cares more about herself and the Doctor than doing what's good? Should she be pitied because of his twisting path and time-line which has blasted every possibility of a normal life from her? Is she too dependent on the Doctor, to the point where he's her only reason for being, and if that's true, should we interpret this as just part of her character, or a bad thing? Or considering that she teaches at a university and willingly breaks in and out of prison, is she independent and free to do as she likes, which occasionally involves the Doctor?
The conventional view of the Seventh Doctor — and certainly the one which carried primarily into the expanded universe — is that he's The Chessmaster, a ruthless Manipulative Bastard who knows all the moves and has the winning gambit planned out before the game's even started, and who's willing to ruthlessly play his companions like pawns. However, if you watch his television episodes closely, you see that for a supposedly hyper-sharp chessmaster he seems to screw up a hell of a lot. Things that he didn't anticipate keep happening, meaning he has to compensate for them. People make moves he didn't expect and hasn't planned for. Sometimes it looks like the villain actually has won, until the Doctor essentially pulls a rabbit out of a hat to save the day. A convincing case can be made that the Seventh Doctor actually sucks at being a Chessmaster, but happens to be excellent at improvisation and for whatever reason is determined to make it look like he knew what he was doing all along.
Similarly, the Sixth Doctor; is he just an arrogant, pompous bully? Or is he maladjusted and riddled with psychological issues from a difficult regeneration — including PTSD — that he never fully manages to overcome?
There is a theory that the experiences of the previous Doctor influence the new Doctor. The 5th Doctor tried to be nice and didn't have a forceful personality, yet his adventures often involved a lot of death. The 6th Doctor might be a reaction to that, he hopes that a reversal of the 5th Doctor's personality will prevent more death and misery.
Or the First Doctor: is he condescending and prickly because he's a weary, Seen It All old man who doesn't have patience for stupid apes and their limited minds, or because he's a rebellious young man who wants to appear mature and important and his treatment of humans is due to the fact that he simply doesn't know any better?
He's said repeatedly in both series that he left Gallifrey because he didn't approve of how the Time Lords treated time and lesser species. Yet he shows an awful lot of those Time Lord traits in early serials until he spends enough time stuck with the human intruders on his ship that he learns to like them and softens up. In later stories, he seems to revert back to a bit of the old Time Lord Fantastic Racism when he's in a really foul mood. So, did he always have the high ideals he shows (or claims) in the later seasons, or merely high ideals by Time Lord standards? Did he have them, then lose sight of them because Susan couldn't challenge him when he crossed the line, as other companions would down the line? Or does he just claim higher ideals and reasons to keep everyone's trust and assuage his own guilt over the violence that follows him wherever he goes? When he excommunicates John Hurt from Doctor-dom, is he ashamed of his actions, or merely hiding from them, pretending they don't exist so he can keep claiming to be the better man?
The Doctor in general: is he closer to several different people who all share the same unbroken set of memories but who have entirely separate personalities, or one person with one overarching personality, whose changes in characterization between regenerations is due to different aspects of that single personality being emphasized or downplayed depending on the incarnation? Viewers who lean heavily towards the second theory tend to be rather befuddled by fans who like one incarnation but dislike another.
"The End of Time" adds a bit of this for The Master, who up to that point had mostly come across as a Card-Carrying Villain with extra Foe Yay, with The Reveal that the drumming that had been driving him insane throughout the appearances of his incarnation played by John Simm was implanted by the other Time Lords as a Gambit Roulette to get themselves out of the Time War. Whether you think this is a Stable Time Loop or not (i.e., the drums were the reason for his insanity in the old series as well) can change him from a borderline Complete Monster who happens to be a victim to a Woobie, Destroyer of Worlds. Though either way, the Time Lords were bastards for doing that to him.
Christina's meant to be seen as a adrenaline junkie Femme Fatale with a heart of gold but can be more easily seen as a borderline sociopath when you notice she had no regrets about getting her partner arrested, is extremely selfish, arguably kissed the Doctor just to manipulate him and only wanted to come along because the police were about to catch her.
Some fans theorize that Rassilon was benevolent at one point, partially because he was one of the founders of Time Lord Society, and partly because there is canon of another Time Lord whose dark side attempted a takeover. On the flipside, while in the canon Time Lord society as a whole certainly thought he was benevolent, but the show itself strongly implied he was just a Not Quite DeadVillain with Good Publicity, with both appearances of the character being egotistical megalomaniacs; it is also speculated / implied that Omega's accident that got him trapped in the Anti-Matter verse was actually engineered by Rassilon himself. The darker views of his character were wholly endorsed by "The End of Time".
Is Timothy Dalton's character really Rassilon fallen to the Dark side? Or is he just an arrogant dictator who took Rassilon's name to make himself sound important? (Bear in mind he's credited not as "Rassilon" but merely as "The President"). Word of God says he's the real Rassilon, having at some point re-emerged and reclaimed control, but since it was never said onscreen Death of the Author applies.
The Bad Wolf. Is it Rose using the power of the time vortex to save the Doctor, or the time vortex controlling the mind of Rose to stop the Daleks?
Or given the events of The Doctor's Wife is it in fact the will of The TARDIS?
Bad Wolf: I want you safe. My Doctor.
The Beast, from "The Impossible Planet"/"The Satan Pit". Is it actually the Whoniverse's version of the Devil, who fought before time against the followers of God, the Disciples of Light, and has inspired all the devils in every religion? Or is the Beast simply an incredibly powerful and evil being who lies to cash in on fears of religion's Satanic figures, so that the scared humans are more easy to defeat and influence? There's evidence for both, and by the end even the Doctor doesn't seem completely sure.
ThisYouTube video of a Doctor Who Confidential offers one for Madame Kovarian: a woman "of a certain age" who never had any children of her own. It seems to be suggesting that not only will Melody/River be raised to be a weapon, but also that Madame Kovarian intends to make Melody/River into something of a Mommy's Little Villain.
In regards to Eleven's treatment of Clara: is he genuinely trying to protect her because he fears her dying again and is still scarred by his separation from the Ponds, or is he being creepy, obsessive, and depriving her of her agency by withholding information she really ought to know. Journey to the Centre of the TARDIS especially divided fans on that last point.
Elton, from "Love & Monsters" - despite several references to LINDA and Clom in later episodes seemingly contradicting this, it is commonly believed that Elton is insane, and is imagining the events of this episode (perhaps in order to deal with his mother's death).
Alternately, the events happened (mostly) as described, but Elton's mind completely shattered was after witnessing Ursula's death and he's simply talking to an empty paving slab, since only he ever sees her, while the camera recording him only sees the slab from behind).
The series as a whole - is it about an ancient alien travelling time and space in a dimensionally transcendent box, or is it about the people who he travels with and how he changes them? Arguments could be made for both sides.
Did the Time Lords grant the Doctor a new set of regenerations out of the goodness of their hearts due to all the good things he's done, or did they do it because the Doctor is the only one who can get them out from where they are now?
The show provides one with the War Doctor. Is he a version of the Doctor who crossed the line, meaning he is the Black Sheep of the Doctors and doesn't even deserve the name? Or is he someone who did what he had to, considering the Sisterhood of Karn told the Eighth Doctor before he made the choice the Universe was being torn apart by the Time War? The War and future Doctors seem to think both. Despite being treated with dread, the War Doctor showed he would only have been reluctantly willing to destroy Gallifrey after seeing he would still turn out good and the Doctor realises on his own he wouldn't have a choice. By the end the future Doctors decide the War Doctor was the Doctor most of all, and he knows he is the Doctor again.
The Sisterhood of Karn. A group of wise individuals in the right place and time to give the Doctor the final push he needed to enter the Time War, or a group of manipulative bastards who engineered the entire scenario to begin with? The audience is never toldwhat caused Cass' ship to crash so close to Karn and it seems highly suspicious that they happened to have prepared all those regeneration potions - including the specially made one for the War Doctor - in less time than it took to retrieve their bodies from the wreckage?
Cards Against Humanity hinted at this trope with the card "A madman who lives in a police box and kidnaps women".
The regeneration between the Second to the Third Doctor was caused directly by the Time Lords as punishment. Much fun can be had trying to Fan Wank out just how much of the Third Doctor's - and, for that matter, the personality of all future Doctors - personality is the Doctor's himself, and how much of it was deliberately engineered by the Time Lords to rehabilitate him... or even to influence him into becoming the Fourth Doctor, constantly used by the Time Lords as a very effective Boxed Crook.
The Telos Novellas like to deliberately stretch the Doctors' characterisations a bit in order to more directly explore what is implied by each Doctor's subcultural theme. For instance, the Second Doctor, who had a Beatles-inspired look, gets to fight evil LSD in San Fransisco in the Summer of Love. The Fourth Doctor, intended as a bohemian, gets a story in which he gets to spend much of the story quoting 19th Century poetry, thinking about 19th Century music and being the kind of main character and having the kind of experiences associated with late 19th Century authors.
The rejected bookCampaign exploits this for Metafiction. Various versions of Ian, Barbara and Susan appear, sometimes even using different names (such as Cliff, Lola and Mandy, or Susan English, or "Dr. Who") or with different professions (one Ian is not a science teacher but a physicist, another Barbara is an art teacher, one Susan is a rocker girl who had a teenage pregnancy, chain-smokes, wears a lot of leather and insists on being called "Sue", and "Tony" and "Amy" are (incestuous) brother and sister. Even within the narrative itself, there are elements of this - for instance, some of the members of the TARDIS crew remember Ian fighting alongside Alexander the Great, genociding innocent people, and have difficulty reconciling this with his usual noble personality. It's a weird book.
The Short Trips story "Nothing at the End of the Lane" is based around the idea that Susan is just a normal child being abused by her mad grandfather, and Barbara finds her murdered at the end before going into a Police Box to call the police. Barbara herself has a mental illness that leads to her experiencing periods of detachment from reality that she calls 'episodes', during which she experiences dreamlike fantasy images of aliens and history.
In the Unquiet Dead, the Gelth - evil conquerors with no regard to sanctity of other life, or just one of many beings driven mad by the Time War, trying desperately to cling to life themselves?
From Big Finish Doctor Who the Neverpeople. Are they a lot of selfish beings who want to take revenge on the Universe for what the Time Lords did to them? Or have they been driven mad by isolation in a timeless universe and do they genuinely think destroying the Web of Time will better the Universe? For all we know not all the Neverpeople agreed to the scheme and it is just being orchestrated by the most zealous.
Are the Divergence a terrifying race that Rassilon locked away to protect his people? Or were they just a potential threat that he overreacted over? The Doctor even points out that Rassilon is trying to destroy them now because of what they'll do to him if they escape.