Gunter

Gunter is the name of the penguin that most commonly accompanies the Ice King, although in "Princess Monster Wife," it is shown that multiple penguins have subtle variants of that name but the Ice King pronounces the other penguins' names differently. The Ice King uses Gunter as his personal servant, whereas the other penguins working for the Ice King are more or less slaves. It is not completely clear whether Gunter is male or female. However, in "The Chamber of Frozen Blades" Gunter lays an egg, which would likely mean it is female.

Episode appearances
In "What is Life?," one of Gunter's known duties is being used as a stand for the Ice King's video game machine. Gunter also tried to warn the Ice King that Finn and Neptr were in the room.

Gunter is mentioned in "What Have You Done?" when Ice King says, "Gunter, dispose of Finn's carcass."

Gunter appears again in "It Came from the Nightosphere," where his/her soul is almost stolen and is dubbed "by far, the most evil thing I've encountered" by Hunson Abadeer, and thrown at the Ice King. The Ice King's response is "Gunter, who told you you could fly?"

Gunter appears in "The Chamber of Frozen Blades" and is very sick, but it later turns out that she was pregnant and the egg hatches revealing a floating pink kitten.

Gunter re-appears in the episode "Still" trying to mess with the potions Ice King brought to freeze Finn and Jake. Ice King says that Gunter likes to break bottles, which Gunter eventually does. She is shown to be a troublemaker in this episode.

Gunter appears multiple times in "Holly Jolly Secrets Part I" and "Holly Jolly Secrets Part II." Notably, during his/her "Penguin Dance Party" video, Ice King calls two different penguins "Gunter" in the same scene. It is unknown whether this was intentional by the show's staff, but this is the main in-show evidence suggesting that Gunter is not a specific penguin.

In "Five Short Graybles," Ice King makes Gunter float out to sea on an iceberg because he believes that Gunter is making his cave smell bad. It also shows that Gunter can play the keyboard, though not very well.

In "Princess Monster Wife," only one penguin is called Gunter and many other penguins are addressed with similar, though different, names.

In "Reign of Gunters," Gunter proves she is the most (potentially) evil entity in Ooo, excluding the Lich, by using Ice King's demonic wishing eye to conquer Ooo and destroy all of its glass objects. At first glance this was a harmless quest for self entertainment, until she tries to break the head of one of the Gumball Guardians, proving that Gunter had no sympathy for those who stood in her way of world conquest. Gunter is only stopped when the Ice King returned from his outing, scolding her for taking his wishing eye and telling her to go back to the castle.

Appearance
Gunter looks like a regular penguin with big black eyes. She/he has a black back, black, flipper-like wings, and a white flat belly. She/he also has a pointed yellow beak and yellow feet with three toes.

Ice King
The Ice King sometimes gets upset at Gunter, such as when he/she accidentally broke his video game or ate his socks, but the Ice King seems to appreciate his/her company. Ice King told Gunter that he loves him/her in "Holly Jolly Secrets Part I." The Ice King often speaks to him/her affectionately like a father. For example, in "What is Life?" Ice King calls Gunter "daddy's little fatty," and he often addresses him/her with terms of endearment such as "honey" or "sweetie." The Ice King likes Gunther as a good pal.

Marceline
As seen in "I Remember You", Marceline waves to gunter and he somewhat waves back, then Gunter sighs, this could mean that Gunter and Marceline could've previously known eachother, either as friends or romantically.

Trivia

 * Gunter is the name the Ice King gives to all of his penguin servants, yet he pronounces it differently depending on the penguin's personality. This is shown in "Princess Monster Wife" when multiple penguins are addressed with some variant of Gunter (e.g. Gundy, Gunder, Gunthy, Goonter, Günder...).
 * One Gunter is the most evil creature that Hunson Abadeer has ever seen, as he claims in "It Came from the Nightosphere."
 * In the episode "Holly Jolly Secrets Part II," BMO deciphers a complicated code in the Ice King's crying, which reveals an image of Gunter when printed.
 * Gunter (variations: Günther, Gunthar) is an old German name made of the words Gund ("Fight," "Battle," "War") and Heri ("Crowd," "Folk") referencing the fact that Ice King calls all his penguins some variant of Gunter, making them his army.
 * Marceline's journal has the name Gunter on it in the episode "Marceline's Closet."
 * Gunter, according to the Ice King, likes to smash bottles and eat socks.
 * Ice King has a picture of Gunter in his diary in "The Chamber of Frozen Blades."
 * In the game FusionFall, Gunter is a supporting character in the game along with Finn, Princess Bubblegum, Jake, and the Ice King. He/she also has an evil fusion counterpart called Fusion Gunter.
 * Gunter's only known weaknesses are Ice King and the squirty-squirt.
 * Gunter's baby has a special fire shooting power.
 * In "Reign of Gunters," Finn, Jake, and the Ice King continuously refer to Gunter as "Gunther," with an "h."