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In "My Two Favorite People", Finn, Jake, and Lady Rainicorn encounter a wizard who is handing out power rings. Finn also wears 10 rings his hands with each one displaying a different power, just like the Iron Man villain The Mandarin.
The robot orb-looking things that Fionna slashes at in "Adventure Time with Fionna and Cake" were based on the farm-intruding enemies from The Legend of Zelda: Majora's Mask.
The episode Mortal Recoil contains a bunch of clear references to The Exorcist and The Grudge.
The tagline for the movie "Heat Signature" is "Under the ocean, no one can hear you die". This is a reference to the tagline for the movie Alien (1979): "In space, no one can hear you scream."
In "Morituri Te Salutamus" just before one of the fighters dies, he says something along the lines of, "Et tu, Verus?" which is a reference to Julius Caesar.
The "Susan Strong" title card is a reference to Lost. There was also a "Lost pan" in the storyboard that got cut from the episode.
Not to mention how Susan Strong & Co also lived underneath a Hatch...
One of the fish people is wearing what looks like a Pedo Bear costume.
The entire memory sequence is a reference to Being John Malkovich, what with the shifting gravity, various doors through memories, and nature of being inside someone's head.
It can also be seen as a refrence to Inception with the extraction of an idea from a dream.
The Lich King, a horned, ridiculously scary, skull-faced monarch who can raise skeletons and whose power lies in a pit of green ooze. The Horned King, a horned, ridiculously scary, skull-faced monarch who can raise skeletons and whose power lies in a pit of green ooze. Welp.
The game Dropball, played by Ghost Man in "Blood Under The Skin," is a Shout-Out to Bullet Ball, the high calibre tablegame designed for the 21st-century lifestyle that went memetic after creator Marc Griffin's memetically depressing/hilarious appearance on American Inventor. Ghost Man's voice sounds quite a bit like Marc Griffin's and several of his lines are quotes from the American Inventor episode.
The episode "No One Can Hear You", references Alien when the candy people are shown to be stuck to the walls of the sewer with a goo, like the Xenomorphs do the their victims. Even the title is borrowed from the Tagline of the movie: "In space, no one can hear you scream." Bonus Points for Finn and Jake screaming in the title card.
On the opposite end of the spectrum, Finn's casts breaking is really similar to Forrest Gump's leg braces.
The music box Finn uses to accompany the lullaby is strongly similar to the Orb of Isis in The Simpsons episode "Lost Our Lisa."
The Bucket Knight is a shout-out to the Alternian Imperial Drones from Homestuck. The artists are confirmed to be fans: a picture of their whiteboard shows doodles of the main characters.
The episode "Wizard Battle", the Grand Wizard states that wizards will fight using the eight schools of magic. This is likely a reference to Dungeons & Dragons' eight schools of magic.
"Five Short Graybles" has Princess Bubblegum making a familiar toothy smile while enthusiastically saying "CHEEEESE".
"Princess Monster Wife" alludes to Perseus and Medusa when Finn and Jake use mirrors in order not to gaze upon the titular monster's hideousness directly, though they are only in danger of fainting instead of being turned into stone.
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