Doctor Who has been around for fifty years. It is inevitable that wham episodes are frequent in its long history. Beware of unmarked spoilers for the entire series up to the recent episode The Name of the Doctor.
The Dalek Invasion of Earth was the first time a companion, Susan, had left. It was also the first time villains from a previous story appeared, and it set up the further Dalek stories. It was also the first story featuring an Invasion, setting this plot up for future stories.
The Chase may seem like a comical and lesser Dalek Story but if you think about the story it is important. The Daleks have created a time machine, so for the first time the Doctor's enemies can time travel and returning to the TARDIS no longer means safety. It also saw the departure of the last of the Doctor's original companions.
The very next story, The Time Meddler, depicted another time traveller from the Doctor's (still un-named) culture for the first time and, for the first time, suggested that it was possible to alter Earth's past history on a large scale.
The Daleks' Master Plan established that the Doctor's companions weren't safe: it featured not one but two companions dying, one of them spacing herself and her assailant in a last-ditch attempt to save the mission.
The Tenth Planet was the first regeneration episode. Basically every fan these days is familiar with regeneration, but the switch from the First Doctor to the Second Doctor must have been a massive Wham Episode for viewers back in the 1960s, especially kids, as the majority of viewers in the pre-Internet age would have been totally unaware the change was coming.
The War Games, where the Doctor is forced to call on his own people to fix a problem for the first time, during which we learn the Doctor is a Time Lord. It ends with the Doctor regenerating again and being exiled to Earth, changing the course of the series for the next three years and beyond. The story also bid goodbye to companion Jamie McCrimmon as a generation of British tween girls wept.
Spearhead from Space is almost a companion to its predecessor in the amount of Wham. The entire starring cast was reset, the Doctor was suddenly on a much more violent adventure, the series is suddenly in color, it was revealed the Doctor has two hearts, and suddenly the space race suddenly had a much more chilling consequence. It also satisfies the "game changing" aspect of the trope by changing the format of the series, with the Doctor now working (and taking assignments from) UNIT, rather than travelling on his own.
Terror of The Autons introduced The Master, brought back the Autons for a very violent exercise, introduced a new companion suddenly (the previous companion being Put on a Bus), along with adding a new cast member slot.
The Three Doctors was a huge example. Not only did it bring back the two previous actors who had played the Doctor, an event unprecedented in television history, but at the end the format of the series changed as the Doctor's exile to earth was lifted.
The Time Warrior, thanks to one word in one line of dialogue: "Gallifrey". Forever more the Doctor's homeworld was no longer a mystery.
Planet of the Spiders. Not every regeneration story must be a Wham Episode, however Pertwee had held sway over the role for five seasons at this point, a record, and for the first time, a young(ish) man was cast as the Doctor, setting a pattern that remained in place until 2013.
Genesis of the Daleks, the first story to feature Davros. Also the events of this episode were cited by Russell T Davies as the first act in the Last Great Time War.
Logopolis. Tom Baker was the most popular Doctor the classic series ever had, so his departure after seven seasons into the (then) youngest Doctor actor ever was a Wham.
Earthshock, both for the Episode One cliffhanger (that Producer John Nathan-Turner took great pains to keep a secret, even turning down a cover of the Radio Times) and for the Episode Four ending, the first time an established companion was killed off.note The two companions who died in The Daleks' Master Plan had each been in the series for only a few episodes before dying. One of them was in the series for such a brief time that the location filming for her death scene was already in the can before they recorded her first studio scenes.
The Five Doctors. The title says it all.
The Trial of a Time Lord episode 13. The Valeyard is really a corrupted future incarnation of the Doctor, employed by the Time Lord High Council to destroy the Doctor to prevent him from revealing their role in the attempted genocide of the human race. The Doctor's only ally in this is the Master, who (obviously) cannot be trusted.
The End of the World, which reveals that the Time Lords and Gallifrey, featured throughout the original series, with the game-changing revelation that the Doctor is (supposedly) the last of his race and that the Daleks were all gone, too...
Until the episode Dalek came along.
The Parting of the Ways was intended to be a bigger wham than it was, as Davies had intended for the regeneration into David Tennant to be a complete surprise, until he was screwed over by the BBC publicity department which prematurely announced that Eccleston was leaving. The moment still packs the punch, as does the episodes revelation as to who and what Bad Wolf is.
Doomsday and the emotionally devastating (for the characters) separation of Rose and the Doctor.
Utopia: You Are Not Alone
Last of the Time Lords, where it is revealed that Jack Harkness and the Face of Boe are the same person.
Partners in Crime. A run-of-the-mill episode goes Wham in its last 2 minutes when Rose Tyler makes a completely unexpected (and unspoiled by the media) return appearance, setting in motion the events of the season finale.
The Stolen Earth in the final few minutes. Rose and the Doctor are reunited- almost, until a Dalek shoots the Doctor. And once Jack, Donna, and Rose get the Doctor back in the TARDIS, it appears he's going to regenerate- the first time a possible regeneration is used as a legitimate cliffhanger.
The Waters of Mars, the Doctor actually does what he swore never to do, and changes a fixed event. After saving people from certain destruction, there's some pretty heavy stuff, including a What the Hell, Hero? from the very people he saved. In fact, the main protagonist he saved commits suicide shortly after so as to maintain the 'proper timeline' leading to an Heroic BSOD.
The End of Time, Part One. That last twenty seconds. The Time Lords aren't just back, they're the ones trying to do as the title says.
The otherwise rather average episode Cold Blood in season five/thirty one/fnarg turned into a Whammer in the last five minutes when yet another companion, Rory, was shot and killed, and then promptly erased by the crack eating up everything in the universe; this made Amy, his fiancée (though she didn't remember it) a more tragic character for the remainder of the season.
The Pandorica Opens. Big time. Where to begin? Rory gets revived after being erased from time, only he's not real; he's an Auton Duplicate! And he ends up shooting Amy, which kills her. Next, the TARDIS exploding is the cause of the cracks in time, and it explodes with River inside, which destroys the whole universe. And to top it all off, the titular Pandorica is actually a prison for the Doctor, and he's been locked inside it, all the while screaming how he is the only person who can stop the TARDIS exploding!
Steven Moffat has managed to write an opening episode absolutely full of Wham - The Impossible Astronaut and Day of the Moon.
The Doctor, in his future, gets shot twice, then again during his regeneration sequence, killing him permanently. The companions know that but the Doctor mustn't know.
The young girl from the Apollo spacesuit is implied to be Amy's daughter. This possibility is made even more confusing by the fact the TARDIS can't determine whether Amy is actually pregnant or not. To top things off, the girl is seen wandering the streets close to death at the end of the episode...and then STARTS REGENERATING! Yes, as in Time Lord-style regenerating.
River kisses the Doctor at the end of the episode, confirming their relationship is DEFINITELY romantic to some degree.
The Doctor's Wife is a Wham Episode for changing forever the context of the TARDIS and establishing without doubt that the ship is a living being.
In The Almost People, it's revealed that the Amy accompanying the Doctor and Rory is actually a Ganger, and has been for some time, and the real Amy is, erm, somewhere, being kept by a Midwife from hell, and about to give birth.
A Good Man Goes to War:
River Song is a mistranslation of Melody Pond, clarifying the "the only water in the forest is the river" line from earlier, and revealing that River is Amy's daughter.
There's a war going on against the Doctor, with Melody/River intended as a weapon to kill him.
At this point, Series Six basically becomes a Wham Season.
Let's Kill Hitler: River is the astronaut that killed the Doctor. And we find out what "Silence will fall" means: Silence will fall when the first question, hidden in plain sight, is asked.
In The Wedding of River Song,we find out that the Doctor who was shot in Utah was actually a Teselecta, that the Doctor's exact relationship with River is that they're married, and that it will be the Doctor who will cause silence to fall. Then we find out that the first question is..."Doctor Who?"
And right at the beginning, Jenna Coleman shows up a good five episodes ahead of her expected debut as a companion. And then her character dies! Or at least seems to.
The Angels Take Manhattan has Amy and Rory kill themselves to destroy the Weeping Angel farm with a paradox, Rory taken back in time immediately after this, and then Amy sacrificing any further time with the Doctor to spend the rest of her life with Rory, after he accidentally gets brought back in time by them. And EVERY statue is a Weeping Angel...actually, that one makes no sense.
The Snowmen. For starters, the new companion, Clara dies, and her Famous Last Words are exactly the same as Oswin in Asylum of the Daleks. Then you find out her full name: Clara Oswin Oswald, proving there is a connection between them. Oh yeah, and there's yet another Clara walking around in the present day!
For longtime fans, also the revelation that the episode is a prequel to twoof the most beloved Troughton episodes, including the one that led to the creation of UNIT.
The Name of the Doctor. While we don't learn the Doctor's name, we do learn that Clara had scattered herself throughout the Doctor's life in order to save him from the Great Intelligence's interference. On top of that, we learn that the Doctor's greatest secret is a past regeneration that did something so awful, he couldn't be called "The Doctor".
The Night of the Doctor, one of the webisodes that was released before the 50th Anniversary special, not only features the return of Paul McGann, but also has him regenerate into John Hurt's Doctor from the end of The Name of the Doctor.
The Day of the Doctor. Gallifrey falls no more. Pretty much every minute of the 50th anniversary special falls into Wham territory, with the ending changing the course of the series in much the same way The War Games and The Three Doctors did.
The Time of the Doctor. A message suddenly broadcasts to the universe and every walk of life seems psyched to figure out what the message is saying. Through this one event, the entirety of Matt Smith's era gets resolved, and as such, spolier protection is enforced herein. We find out who blew up the TARDIS, what the Doctor's greatest fear was in The God Complex, the purpose of the Silents, the significance of The Question and "Silence Will Fall", what Trenzalore is, and why it will fall when the Question is asked.
The Doctor has feared the return of the cracks most of all and finds one last crack left that leads to the universe with Gallifrey, and through it, the Time Lords are calling out, "Doctor Who?" to be sure it is safe to return. But the crack is inside a town where a Truth Field prevents people from speaking falsely, so he would have to say his name and wholly confirm the path is clear. And when he translates the message, which is being listened to by all parties, it allows everyone to know the truth.
Except... Gallifrey has no choice but to blindly transmit its distress signal in desperation of survival. It spreads across the universe and draws in its enemies, who would instantly make war if the Time Lords came back, so the Doctor fights off all of them for centuries. That constitutes Daleks, Cybermen, Weeping Angels, Sontarans, and many others.
Tasha Lem and the Papal Mainframe try to keep Trenzalore shielded, but the Daleks have already taken control. After many epochs of fighting against the Doctor, the Silents of the Church join forces with him when he frees Tasha from Dalek control. The Daleks are the only race that do not give up the fight, being the greatest and most tenacious enemies of the Doctor and his species, who have plenty of bones to pick with them and refuse to let the Time Lords return.
All the while the Doctor keeps trying to drop off Clara safe at home on Earth, as he ages into a very tired old man... who is out of regenerations.
Tasha pilots the Doctor's TARDIS back to Earth so Clara can see the ancient Eleventh Doctor and say goodbye as the Daleks close in on the dying man. She pleads into the time crack for the Time Lords to help the Doctor in his hour of need and tells them that his name IS "the Doctor" and if they love him, they need to save him. Cue the time crack being shifted into the night sky above Trenzalore and spitting out a brand new regenerative cycle into the Doctor. He then begins a rule-breaking thirteenth regeneration which, as a result of going past the safety governor of twelve regenerations, is out of control, smiting every Dalek surrounding Trenzalore into oblivion, including a freaking warship as the Doctor weaponizes the energy. Much destruction ensues in Christmas town from the final strike, but they will rebuild.
Clara finds the Doctor back in the TARDIS after the big brouhaha regeneration- and he's young again! But... the regeneration's not done yet... it's just the reset caused by gaining the new cycle and the main event is yet to happen. He gives a heartfelt speech about how this change will be good as long as he remembers who he was as this incarnation, and has a final goodbye with Amy Pond in his mind- whether or not it was just a hallucination or something more... who knows?
Eleven gets a rousing closure, parts with his bow-tie to move on and become a brand new incarnation, unlike the way he got sentimental as Ten, then regenerates in a fashion best described as sneezing himself into another body, and he suddenly realizes he's now the Twelfth Doctor. And has new kidneys... in a color he doesn't like. But the biggest shocker? The regeneration trauma has scrambled his memory, so as the TARDIS begins to crash out of flight for some odd reason, Clara must now jarringly adjust to a totally different Doctor... who has no idea how to fly the TARDIS.
Alien Bodies has reveals in the future the Time Lords will be in a war they are losing, it introduces Faction Paradox, and involves the Doctor's corpse.
The Shadows of Avalon has the Doctor's TARDIS apparently being destroyed and Compassion mutating into one.
The Ancestor Cell resolves the Eighth Doctor Adventures' Time War plot and, for the first time in any medium of Doctor Who, destroys the Time Lords.
The Time of the Daleks ends with the realisation that something is wrong with time and it involves Charley.
Neverland ends with the Doctor infected by Anti-Time and becoming... ZAGREUS!
Zagreus has the return of Rassilon and ends with the Doctor being exiled to another Universe, one without time.