Ice King's crown

The Ice King's crown is the source of his Ice Powers. The crown is golden, topped with three points and adorned with three red gems. One of the gems within the crown protects Ice King from the evil brainwashing spells of the Lich.

History
In "Holly Jolly Secrets Part II" it is revealed that long before the setting of the story (probably before the Mushroom War), when he was still a human named Simon Petrikov, Ice King purchased the crown in Northern Scandinavia from "an old dockworker" as a part of his studies to be an antiquarian of ancient artifacts. He rushed home to his fiancée Betty and put it on in an attempt to make her laugh. While wearing it, Simon experienced visions, which he frantically fought with and shouted at. He also underwent a personality change that he apparently couldn't remember afterward. He realized the crown was doing these things to him and took it off quickly, only to find his fiancée terrified and looking at him with "such contempt." She soon left him. After repeated exposure, the proto-Ice King developed his Wizard Eyes and his body underwent radical changes with subsequent use of the crown. The visions he gained told him that the crown would "protect" Simon "with its frost," though he didn't know what this meant at the time. His skin turned blue, his nose grew long and pointed, his body temperature dropped to around 30 degrees C, his hair and beard grew long and white. Simon realized that the crown's effects were becoming permanent, but knew he was "too far gone" to do anything. After the first time he put on the crown he started a series of videos chronicling what had become of him, in hopes that one day someone would help him to free himself from the things the crown was doing to his mind. The crown causes Ice King's emotional confusion and madness, in contrast to Simon's calmness and intelligence.

In "What Have You Done?," Ice King mentions that he did not steal the crown, although he did make it with stolen magic. It is proved that this is untrue, as stated in "Holly Jolly Secrets." Adam Muto commented Ice King is an unreliable narrator and disassociated from the past of Simon Petrikov, so he presumably does not remember where he got the crown and simply made up the fact that he made it himself. Another possibility is that due to long contact with the crown has caused some of its memories to rub off on him; being totally amnesiac, he may have assumed it was one of his own memories. In the episode "The Lich," Ice King has one of the gems used to unlock the Enchiridion's true power. It's not known if this gem is also the source of the crown's other abilities or its ability to keep the Ice King alive.

In the episode "Finn the Human," Farmworld Finn puts on the crown, causing him to go insane and have a desire to freeze everything he can, all under the crown's sentient influence. It also causes his hair to grow rapidly, as it did to Ice King, and his hair is used to fly by flapping like wings, similar to the Ice King's beard. It is shown again in this episode that the crown is fully sentient, as it becomes grieved by Simon's death and retaliates by freezing the planet for 400 years.

Abilities
The Ice King's crown is show to possess immense magical properties, such as granting the wearer control and manipulation over ice and snow.

The crown also gives Wizard Eyes so that the wearer may see spirits of the Spirit Realm. This is also stated in "Holly Jolly Secrets Part II" when Simon said he was starting to see strange visions.

It also seems to gives its wearers ability to hear voices of the snow. As in "Jake the Dog" where Farmworld Finn mention the age of ice and whispering snow.

It additionally seems to have the capability to keep the wearer alive regardless of age. This is suggested in the Adventure Time episode "Simon & Marcy," when it is revealed that Ice King is 1,043 years old.

The crown also seems to have some sort of addictive effect of the mind of the wearer, creating a desire to wear the crown, using its powers more and more until the identity of the wearer is subsumed within the crown. The danger of using the crown and the subsequent powers it bestows is evident when Simon becomes more and more "weird" after each successive use, until he becomes the Ice King. However, the rate at which the crown  reduces its wearer's sanity is proportional to how much resistance is offered to the whispers of power emanating from the crown. When Farmworld Finn puts the crown on and uses its power to exact revenge on the Destiny Gang and save his family, he willingly embraces the icy power of the crown. Simon Petrikov directly resisted the crown's influence, thus allowing him to retain his sanity for a longer period of time. It is unknown who or what made it, or even how the crown was made, although Ice King claimed it was made from "stolen magic" in "What Have You Done?"

Sentience

 * "..I see the visions always whether or not I wear the crown. They tell me the secrets... the secrets of the ice and snow... that the power of the crown will save me with its frost."

In "What Have You Done?" the crown is shown to speak and feel regret in the scene where it cries on the Shelf of Penitence. It has a feminine voice.

In "Finn the Human", Farmworld Marceline stated that the crown had frozen the world in its grief.

In "Simon & Marcy," Ice King refers to young Marceline as Gunter multiple times, showing another possible effect of wearing the crown: forgetting names, and instead naming people and animals a different name (which in this case is Gunter). This may also be the reason why Ice King's penguins are all (often interchangeably) named Gunter, albeit with several different variations and pronunciations.

The transformed Simon, who was partway Ice King, has been heard on multiple occasions calling Betty his 'princess'. He does so in a frantic state while searching for her, and later when recording a video lamenting that he never found her. This may also be a side-effect of the crown, as opposed to a pre-existing nickname he had for Betty, as there is no evidence of him calling her that prior to her wearing the crown.

The consistent occurance of these two names is that he has called things in a parent-child relationship Gunther, and those he pursues romantically 'Princess'. As the crown has been indicated to feel emotion, speak and communicate in images, these could be involved in the conveyance of these titles.

Trivia

 * The gender-swapped version of the Ice King's crown is a tiara, as tiaras are worn by female Ooo royalty. Ice Queen referred to it as a tiara when it was knocked off her head in battle in "Fionna and Cake."
 * In "Fionna and Cake," Fionna smacks the tiara off Cake's head, saying "You'll catch her crazy!" Since Ice King wrote this fanfiction, one can speculate that somewhere deep down in his psyche, the Ice King may know that the crown can drive someone mad.
 * Jake has been seen wearing the Ice King's crown in the episode "Thank You," though it had no effect. This is because Jake is already magic, according to Adam Muto. Since Cake was able to use the Ice Queen's tiara, it is likely the Ice King is unaware of this fact, or else he made the fan fiction before "What Have You Done?"
 * However, in the episode "Holly Jolly Secrets Part I," Gunter is seen wearing the crown and is also unaffected by its powers.
 * In "Earth & Water" Gunter (still unaffected) is seen to be using the crown's powers to make a species of snow-snake.
 * In the short "The Wand," Ice King's crown has five points for a brief moment after he sacrifices himself to stop the magic wand.
 * In "Holly Jolly Secrets Part II," it is shown that Ice King was using the crown over an extended period of time before the physical changes and control of the crown started, but in "Jake the Dog," Farmworld Finn instantly grows paler, and shows rapid hair growth, and immediately shows a decent amount of control over the crown's powers, and turns his voice into a raspy one. Simon resisted the crown's influence, and Farmworld Finn embraced it in order to save his family.
 * Before he reached the state he is currently in as "Ice King," every time Simon wore the crown, his hair and beard would suddenly grow longer. However, when he removed the crown, his hair and beard would grow back to its normal length.Tumblr_ms5qg3kae91rm7i00o6_1280.jpg
 * Simon once used the crown as a weapon by smacking his enemy with it.
 * The crown's only known purpose seems to be to protect whomever wears it. This is implied in "Holly Jolly Secrets Part II," where Simon Petrikov says that the voices he hears while wearing the crown tell him that the crown's power will save him. In "Finn the Human," after Farmworld Simon Petrikov was killed by the mushroom bomb, the crown grieved the loss of its master and retaliated by freezing the entire planet. However, this protection is clearly something of a Faustian bargain, as it comes at the cost of the wearer's sanity. Simon still exists inside of the Ice King (otherwise the crown would have failed to protect him) but is incredibly suppressed, almost to the point of non-existence.
 * In the comics, the Ice King also has another spot for another gem on the inside of his crown. It is currently unknown what the purpose of this gem is.
 * It seems that the crown has a sort of "Symbiote" relation with the host, feeding on it's sanity and in exchange giving the control over the ice and snow while protecting him; the physical changes could be a side effect.
 * In "Betty," it is shown that the crown's jewels turn gray when drained of magic.
 * The crown is similar in many ways to the One Ring of Sauron from J.R.R. Tolkien’s Lord of the Rings: it grants the wearer magical powers, protects the wearer from aging, warps the wearer’s personality, and its use is addictive.