Son of an Ape

"Sad, that I must litter space with ape corpses."

—Baktosh "Redclaw" nar Kiranka, Wing Commander

Generally in sci-fi/fantasy settings where there are other non-human sentient species, they will often refer pejoratively to humans as apes or monkeys. Sometimes, even a human is seen doing this. More likely to happen in settings where humans are depicted as being less intelligent or civilized than other sentient races.

The Big Bad tends to do this often if he's not human himself, or if he is not human anymore.

Despite this trope's use of the word "ape" as an insult, it should be noted that biologically, humans actually are a species of ape and a type of Monkey (specifically an Old World Monkey, due to our species arising in Africa, an Old World continent). The insult implies that the human in question is uncivilised and therefore cannot be distinguished from an ape. Compare Neanderthal.

A subtrope of Fantastic Slur.

Practically speaking, as much as morally, it should be the other way around, as pointed out by many animal rights groups. Gorillas especially are mind-bendingly clever, able to disarm human traps made by poachers and empathetic enough to want to protect the human rangers who were themselves going to disarm the traps (see Real Life examples - or rather, the ways real life averts this trope - for more).

Examples of Son of an Ape include:

Anime and Manga

In Dragonball Z, Frieza is very adamant about the Saiyans being "mere monkeys" even when he's getting his ass kicked by one. Indeed, having tails even when not transformed, they are technically monkeys rather than apes. Not that it reduces the Fantastic Racism any. And Frieza isn't particular. He uses all variations of "ape" and "monkey" to insult the Saiyans.
In Love Pistols, zoomans (humans developed from other animals than apes) use the word "monkey" sometimes neutrally, and sometimes as a slur.
In episode 5 of FLCL, Haruko insults Amarao with something along the lines of "primitive monkey!", to which Amarao responds that it is politically incorrect to refer to "underevolved species" that way.
In the first half of Tengen Toppa Gurren Lagann, Viral consistently refers to the human heroes as "naked apes", as do Generals Adaine and Cytomander. (Thymilph isn't around long enough to do it and Guame presumedly knows better.)
In Getter Robo, the Dinosaur Empire refers to humans as "arrogant apes."

Comic Books

From New X-Men 130:

Xavier[addressing human troops]: The X-Men have this deliberately engineered "emergency" under control. We've just lost one of our rescue team, do you understand? We're in no mood to play chimpanzee politics...

Fan Works

The Buckaroo Banzai example below is invoked for humor value in this vignette from Girls, Girls, Girls, a parallel subseries of the Mega Crossover Drunkard's Walk, when Buckaroo's daughter explains to monkey faunus Sun Wukong that Remnant's "not our damn planet, Monkey Boy".

Film

The Black Hole aliens from the Godzilla series refer to earthlings as primitive apes, despite the fact that they themselves look like gorillas.
In The Adventures of Buckaroo Banzai Across the 8th Dimension, the Red Lectroids insultingly refer to human beings as "monkey boys".
Men in Black: The Bug calls humans "monkey boys", which is almost certainly a Shout-Out to Buckaroo Banzai.
The angels in the The Prophecy series constantly refer to humans as "talking monkeys".
Alluded to in an inversion of sorts in Planet of the Apes quite a few times. Notably verbalized in Zira's comments like "You know what they say, human say, human do." and "to apes, all men look alike."

Literature

In The Hitchhiker's Guide to the Galaxy, there are several pointed references to humans being descended from apes, and more than one character addresses or refers to Arthur with some variation of "monkey man". What they're descended from isn't mentioned.
Mendoza, an immortal human in The Company Novels, refers to normal humans as monkeys.
During the Man-Kzin War period of Larry Niven's Known Space series, the Kzinti constantly referred to humans as "monkeys". By the Ringworld period, they have stopped doing that, having had their collective asses handed to them too many times by the humans to casually dismiss them anymore.
- The monkey comparison is occasionally presented by the narrative as being a positive one, in that as monkeys we have curiosity, which leads to learning potentially valuable things that the feline Kzin do not. Clearly they never heard that cats are curious too.
In Starship Troopers, the Drill Sergeant Nasty frequently refers to his recruits as apes to motivate them. This is not unknown in Earth's military history.

Come on, you apes! You want to live forever?

Used frequently by Mudge in reference to Jon-Tom in Spellsinger. Also on one occasion by Dorcas the hinny.
- Given that monkeys in Mudge and Dorcas's world are fully sentient and civilized, the implication may have been that Jon-Tom is foolish or frivolous rather than primitive.
In the Codex Alera, one of the Canim insults the human protagonist with a phrase that roughly translates to "monkey-boy". The spirit of this trope when turned on another species is also seen in that the worst insults you can offer a Cane are "dog" and especially "jackal".

Live-Action TV

The Ninth Doctor from Doctor Who refers to humans as "stupid apes" on several occasions.
- As do the new series' Silurians, some of whom want to wipe humanity out.
The Xindi from Star Trek: Enterprise refer to the humans as being "ape-like". In this case it is generally intended as more descriptive than insulting, and the same term is also used for Primate Xindi.
Uriel on Supernatural refers to humans as "mud monkeys." Lucifer condemns humans for being "murderous hairless apes".
The Cat on Red Dwarf calls Lister, Rimmer, and Kochanski "monkeys" on a regular basis.

Music

Crash Test Dummies' "Superman's Song" contains the line "dumb as an ape".
The Tool song "Right In Two", which is sung from the perspective of angels, refers to humans as monkeys.

Newspaper Comics

In Sherman's Lagoon, the characters refer to humans as "hairless beach apes".
In one Calvin and Hobbes strip, Calvin asks whether Hobbes believes that humans evolved from apes. Hobbes' response: "I sure don't see any difference."

Tabletop Games

In Warhammer 40,000, the Eldar derisively refer to humans and other species they deem inferior as "mon-keigh". It only sounds like "monkey," though; the meaning is "those which have to be exterminated."
In the Shadowrun setting, a trideo program out of Tir Tairngire had an elvish title that translated as "Keeper of the Monkey House". It's a flagrantly-racist comedy about an elven landholder's dealings with idiotic, destructive, irresponsible human tenants.

Theatre

In Princess Ida, Lady Psyche teaches that all men, as opposed to women, are apes at heart:

For the Maiden fair, whom the monkey craved,
Was a radiant Being,
With a brain far-seeing --
While a Darwinian Man, though well-behaved,
At best is only a monkey shaved!

In The Hairy Ape by Eugene O'Neill, the Anti-Hero "Yank" takes being called an ape so seriously that, by the play's final scene, he wholeheartedly believes he is one.

Video Games

In Wing Commander the felinoid Kilrathi refer to the humans as "hairless apes" and similar terms.
In Chrono Trigger, Azala refers to humans as apes.
Sword of the Stars, the nickname for humans is 'ape' or 'monkey'. This nickname was originally used by the Tarka, but was adopted by most major species—including humanity itself. That said, most of the species from Sword of the Stars have similar nicknames: Tarka are 'crocs' or 'lizards', Hivers are 'bugs' and Morrigi are 'crows'. The Liir probably have one too, but it's not mentioned. As for the Zuul, they have no name for themselves. Zuul is just what the other races call them, which is a Liir term derived from the word "Suul'ka", meaning "abominable" (any further epithets would probably be redundant).
Sakuya does this to the heroine a few times in Hatoful Boyfriend. The heroine can return fire with poultry comments. This stops being funny in certain storylines.

Web Comics

In Homestuck, unusually, it is some of the humans who refer to themselves this way when talking to trolls (John calls human babies "little pink monkeys", and Dave refers to the human civilization as growing from the foundations of simian reproductive potency.) Only once Gamzee calls Dave the "pInKeSt oF MoThErFuCkIn sTaR MoNkEyS".
"Hairless apes" from Twokinds
In The Gutters the shark refers to humans as "hairless monkeys".
Artie the uplifted gerbil in Narbonic occasionally refers to humans as "plains apes". This has been taken up by many of the transgenic community in Skin Horse.
In The Inexplicable Adventures of Bob, aliens sometimes call us "primates" or "bald monkeys" or such, but more often they deride us for being vertebrates, since the Nemesites and Ipecacs are arthropods. Riboflavin calls Bob a "verminous little spine thing" at one point.

Western Animation

On Futurama, Nibbler describes Earth as being ruled by "psychotic apes".
On Crash Nebula, the Show Within a Show from The Fairly OddParents, the kid who will grow up to be Crash is repeatedly insulted by the other space students calling him one variation or another on "moderately evolved primate".
In Megas XLR, Gorrath calls humans "monkey men".
"Grab that rope, you hairy ape!"

Aversions in Real Life

See Snopes for more on the aforementioned gorillas disarming traps. Reportedly they even wanted to keep rangers away from the traps to protect the humans!
Scientifically, there is no reason any lifeform can't have any biologically-derived trait simply because humans also have it, so to differentiate between different species of primates in a derisive way and between "dumb brutes" and "smart in-groups" isn't just illogical and immoral, it misses the point of classifying species in the first place; It's a library catalogue, not a soapbox, and the truth will always be that we humans are all monkeys at heart and there's nothing wrong with that!
- Sadly, this can include objectively bad traits, at least as far as non-humans having human traits goes; Chimpanzees have been observed being very territorial and frequently fight tribal wars, and don't seem very keen on recognizing us as living beings that don't want to feel pain regardless of if we encounter them in zoos, in laboratories or in their natural habitat. To say they're "evil" is incorrect and somewhat hypocritical (to be fair, to them a smile is a death threat, and we know surprisingly little about Chimpanzee behavior when they don't think we are present and watching; an important distinction to make for seeing what an "animal" as intelligent and social as Pan Troglodytes is like in the wild), but from observation they appear as very much a surprisingly intelligent yet highly aggressive species with an often ruthless hierarchy that produces very little social equality amongst themselves. In the long run, from what we know about them, giving them their space is probably the best and kindest option... maybe someday they'll grow out of it too.