"Mortal Folly" was the first truly serious episode of the series. It featured the Lich, a villain bent on killing everything in Ooo, and/or the world. The battle with the Lich lead to numerous future plotlines and episodes, containing a great deal of inter-episode continuity and a lot of character development, including a falling out between Finn and Princess Bubblegum.
At the time, "Mortal Recoil" was a major wham episode, as Princess Bubblegum was reverted to thirteen years old.
"Too Young," the sequel to the "Mortal Folly/Recoil" 2-parter, was a Wham Episode, because it led to the princess turning eighteen again, the first instance of the Finn+Bubblegum romance being squashed. It also introduced Lemongrab, who is the show's biggest example of Princess Bubblegum's harmful, scientifically unethical side.
"Holly Jolly Secrets Part II". After 20 minutes of Finn and Jake watching the Ice King's awkward and goofy video diary, we're suddenly thrown into an Apocalyptic Log chronicling the creation of the Ice King: He was originally an actual human professor, Simon Petrikov, from before the Great Mushroom War who slowly fell into insanity after buying a strange crown from a Scandinavian merchant, causing him to lose his fiancée Betty in the process. The crown gradually turns him into a blue freak with magic abilities, thus he survives the Great Mushroom War and ends up the thing he is today. He doesn't want to hurt anyone; he just wants Betty (who he called "his princess"). Though he alluded to remembering his past, by "I Remember You", Ice King doesn't even remember it when he's told about it. This gets referenced repeatedly throughout the rest of the series.
"In Your Footsteps" was a Wham Episode when it first came out, definitely. The episode starts off heartwarming and pretty silly, then it's revealed that the Lich has the Enchiridion.
"Incendium", of course, scuttled the whole FinnxBubblegum idea with the introduction of Flame Princess.
In "Burning Low", Princess Bubblegum reveals why she had Flame Princess trapped in the lamp: because if her elemental matrix were to be subjected to too much romance, she may well destroy the earth. This almost comes true, but it's apparently subverted at present by Finn and Flame Princess simply not kissing (directly).
In "Lady & Peebles", Lady Rainicorn reveals to Jake that she is pregnant. The page image is Jake's reaction.
"I Remember You" was indeed one. Marceline knows Ice King and knows what he's gone through. She tries to make him realize how tortured of a past he has and gets frustrated and eventually tears up over it. It's also revealed that Marceline received Hambo, her greatest treasure, from him. It's also revealed in a Freeze-Frame Bonus that Ice King discovered the Enchiridion. There was a newspaper headline that said, "Simon Petrikov Unearths Ancient Treasure."
"The Lich" was the show's fourth season finale. All of the gems on the princesses' crowns? They're magical artifacts that not only protect themselves from the Lich, but also fit into secret holes in the Enchiridion, found by turning the little sword on the book. Oh, and about the Enchiridion? That book that Finn uses to sit on wet grass? It's actually an extremely powerful artifact that allows the user to warp between different dimensions. Booko explains that there exists a multiverse in which universes are randomly connected with naturally occurring worm holes or artificial worm holes created by a powerful artifact—like the Enchiridion. At the end of the episode, the Lich (who was disguised as Billy, and was later confirmed to have killed him and taken his skin) tricks Finn into opening an artificial worm hole into another universe by destroying the book. After the boys enter the worm hole, the last scene shows Finn as a farm boy, and a normal dog named Jake, being called over Finn's human mother. This episode then leads into two additional episodes, making it a three-parter (with an inter-season cliffhanger) with "Finn the Human" and "Jake the Dog", which also call back to all the previous episodes involving the Lich King, as well as the Ice King and Marceline's background.
The storyboards for The Lich contain a twist that didn't make it into the final episode: the Enchiridion reveals that Finn's biological father is alive and wrongfully imprisoned inside an alternate dimension with all of the multiverse's most evil criminals, where he has apparently taken up kicking everyone's ass. Oh and Finn never knew that he was adopted. And Jake never told him. Yeah. Parts of this scrapped scene were reused for the season five finale and season six premiere.
"Be More" is a Wham Episode because we finally get to see BMO's family, and we finally get to see Finn meeting another human. To be exact, human turned cyborg since he predates the Mushroom War. This human also happens to be BMO's creator.
"Sky Witch": Marceline finally get Hambo back after trying to track the witch for so long, though only because Bubblegum sacrificed the homemade t-shirt Marceline made for her to trade for it. What's more said sky witch, Maja, plans to use the t-shirt in a spell since it contains much more personal attachment then Hambo did. For what though, we'll have to wait and see. The only clue we get is that it'll be "something big".
"Frost and Fire" is a Wham Episode as, after a long, awesome battle between Flame Princess and Ice King, it ends with The Ice Kingdom destroyed and Flame Princess breaking up with Finn because he seriously hurt her feelings.
"Too Old" is a Wham Episode because Lemongrab backslides into full-blown villainy and eats his brother alive. Not to mention the episode being filled with several scenes of graphic child abuse and domestic abuse, all played for straight-up horror and tear jerkers.
And as for fans of the Finn x Bubblegum pairing, the bottom of the ocean where that ship sank in "Too Young" and crumbled in "Incendium" pulls the wreck even deeper into the abyss.
"Earth And Water" completes a recent row of wham episodes. We learn the real reason Flame Princess was locked up for most of her life (which involved her own father trying to have her tossed in the woods to die) and Flame Princess and Cinamon Bun stage a coup in the fire kingdom and trap Flame Kingin the prison he kept FP in, with Flame Princess becoming the ruler of Fire Kingdom. Finn and Flame Princess patch things up and while they aren't quite back together yet, it seems they're on the way to repairing their relationship.
"The Vault" sees the return of the Green Lady(real name Shoko), who was a friend of Princess Bubblegum and witnessed the rise of the Candy Kingdom. Did we mention she was a past life of Finn, who lives in the tree that Shoko died next to? It all works out. No wonder Jesse Moynihan (storyboard artist/writer for this episode) was expecting a big response from this episode.
The Bath House Gang's headquarters is identical to the mansion from "The Creeps," (where the Green Lady first appeared) and also identical to the Destiny Gang's hideout from "Finn the Human." In other words, Jake was almost right when he said Finn was imagining the Green Lady's appearance in "The Creeps". Finn was actually having a distorted vision from his past life.
Although it's been pretty much confirmed already through hints and clues, this is the first time it's been outright stated/demonstrated that Princess Bubblegum is centuries older than her physical age. They even revealed it all dramatically with PB taking off her hood at the beginning of the flashback.
The amulet will probably show up again.
At the end of "Play Date" Keeoth (the demon whose blood Joshua used to create the demon-blood sword) returns when Ice King reads demonic runes on the sword. When Finn and Jake show up, Keeoth still thinks Jake is Joshua and demands that he return his blood to him. Finn and Jake try to chant the magic words to banish him, Keeoth threatens to kill Ice King and Abracadaniel. Finn has no choice but to destroy the demon-blood sword, returning Keeoth's blood. After Keeoth promises to leave, "I Lied" comes into effect and Keeoth grabs Jake and disappears, ending the episode.
"James": Finn, Jake and the titular James (a goofy candy person) join Princess Bubblegum on an expedition when they are attacked by goop zombies. When all escape attempts have failed, James sacrifices himself to save the others. The episode ends with Bubblegum cloning another James. But meanwhile, the original James, now a zombie, crawls out of the pit, followed by more zombies. That's one hell of a Cliff Hanger.
Not an actual episode, but Adventure Time: Explore the Dungeon Because I DON'T KNOW! is a game where the final boss is a bubblegum blob monster that is actually Princess Bubblegum's parents, and the princess in question is 827 years old. Pen Ward has confirmed this info as a part of the series canon.
"The Red Throne": Flame King escapes and has his partner, Flame Lord, drug Flame Princess and force her to marry him. While Flame King is once again imprisoned, any chance for the Finn/Flame Princess ship is utterly dashed into pieces by Cinnamon Bun of all people, who admits his feelings for her.
Cinnamon Bun also becomes fully baked (it was previously mentioned he was only half-baked), and now displays much more intelligence and capability than ever before.
"Betty": The release of an Anti-Magic being causes the Ice King's crown to lose it's magic, turning the Ice King back into Simon. Without the Crown's magic, Simon begins dying. He asks Marceline, Finn, and Jake to help him say goodbye to his fiancee Betty. With the sacrifice of Hambo, Simon opens a Portal to the Past...but Betty isn't content to say goodbye and jumps through the portal into present day Ooo. Betty then defeats the Anti-Magic being, which restores Simon's life and powers but also turns him back into the Ice King. Betty endeavors to find a cure for Simon's curse and begins wandering Ooo.
"Billy's Bucket List": Finn gets over his fear of the ocean to honor Billy's bucket list wish of floating in the ocean. By doing so he sees a vision of Billy in the stars, like Mufasa from The Lion King who tells him that his human father is alive in the Citadel.
"Wake Up": Prismo is killed by the Lich, who is transported with Finn & Jake to the Citadel, revealed to be a prison for beings who have committed crimes on a cosmic level.
"Escape from the Citadel": The Lich destroys the Citadel and its Guardians and the five surviving inmates escape along with Finn's dad, who abandoned Finn again. Finn defeats the Lich by throwing the Citadel Guardian's healing blood on him, reducing him to a harmless infant. Finally, Finn loses his right arm, following two seasons of foreshadowing.
"The Tower": Although he fails to build a high enough tower to space, Finn gets a glimpse of that portal from the Citadel, which implies that Martin and his alien crew went in the direction of Earth.
"Breezy": After learning that his flower arm is dying, Finn tries to get back in the dating game with a bee named Breezy helping him (because she's in love with his flower arm). At the end, Breezy somehow manages to regenerate Finn's original arm.
"Joshua and Margaret Investigations: We learn that Jake was born not from Margaret's womb, but from a weird egg that sprouted from his father's head after he got bitten by a shape-shifting monster, which makes him a half-monster hybrid. This also explains how he got his stretchy powers.