A very prevalent notion in modern society is the idea that black men are better endowed than other races. The stereotype is a very old one, likely centuries. While... kind of... an example of Positive Discrimination, it has some negative consequences, and quite a checkered past.
Since the colonial era, there has been the idea of a well-endowed, sturdily built, and rather libidinous black man. Until the late 20th century, it was commonly accepted that black men made no effort to control their sex drives, and, in some time periods and regions, a lot of nasty stuff was done on the paper-thin excuse that the victim had posed a sexual threat to someone, often a white woman. (Needless to say, very little was offered in proof of any of these allegations).
The stereotype of black men as oversexed is, at root, dehumanizing. These are not rational creatures like white men, it claims; these are brutes or animals whose sexual functions operate mechanically and instinctively like a bull in rut. The female side of the equation didn't escape this either. The rape of slave women by white overseers or plantation owners was 'justified' on the belief that black women were "hot" and needed the sexual control of their white masters. As for white women, "Once you go black, you never go back" implied that they were considered Defiled Forever if a black man got their hands on them (willingly or not). And heaven help the mother of a Chocolate Baby...
In other words, this trope has extremely unpleasant roots, and continues to be played in insensitive ways. You Have Been Warned.
In case you really want to know, a not-particularly-scientific survey found that "[t]he average for the African continent as a whole is a whopping 6.3 inches."
Obviously a subtrope of Bigger Is Better in Bed. See also Where Da White Women At?
Jaakko Teppo tells a self-admittedly dirty joke about a racist guy in Tampere who has just met two black guys on Tammerkoski bridge and is telling his friend all about it:
"And they go on to piss off the bridge, and this one n***r says, Aw shit, man, is the water cold today, and the other one says, And the bottom's muddy too, dammit!"
Russell Peters has a bit where he talks about God addressing all the races. First he tells the Indian people that they will be great with computers, be able to thrive in some of the harshest conditions imaginable, and then leave those conditions to become successful anywhere in the world. They don't care about any of that and only want to know how big their penises will be. God apologetically tells them "average". Then he takes the black people aside and tells them that they are going to be mistreated and discriminated against for centuries, so he's giving them a little extra penis size to make up for it (he took it from the Indians).
Sometimes this trope refers not so much to any specific part of the anatomy as to sexual prowess in general. In Enter the Dragon for instance, the black bruiser Williams is among the martial arts contestants offered some feminine "company" for the evening from Han's Paid Harem. He picks out four of them, and then apologizes to the rest of the girls that, um, he's "a little tired" this evening.
In the original script, this was followed by Sheriff Bart saying, "I hate to disappoint you miss, but you're sucking on my arm."
In another scene:
Charlie: They said you was hung.* Charlie means "hanged," the proper past tense of "to hang" in the sense of an execution.
Bart: And they was right.* Bart doesn't.
At one point in the Vietnam epic Full Metal Jacket, a hooker initially refuses to sleep with an African-American man because of his so-called "Alabama blacksnake". Subverted, as the soldier in question whips out the snake in question to prove that "it ain't too God-damn beaucoup!"
Referenced in Gutterballs, when a character is looking over the brands offered by a condom machine.
How about Black Knight? 'For the Big One?' That's for big black cock, that's gonna fall off me for sure.
In Liberty Heights, a teenager tells his friend that somebody saw the new black kid in the shower and he was huge. However, it's unknown if that is true or just gossip.
Horse is rather concerned when he learns of the plan to strip completely, because he thinks everyone will expect him to be well-endowed where he's merely ordinary. Guy, a white guy, is the one who proves to be particularly well-endowed instead.
Gaz (upon seeing Guy's "assets" at the tryouts): Gentlemen, the lunchbox has landed.
Also subverts it, in that Dave asks his wife whether, were anything to happen to him, she might take up with a black feller. She answers that she "might do, yeah." He immediately goes into a funk, because everyone knows they have "great bodies and that." However, he actually is talking about their entire physiques in general and not merely their equipment, because he's very insecure about his own appearance.
Harold: I don't understand how you can be so calm about all this.
Tarik: Look at me. I'm fat, black, can't dance, and I have two gay fathers. People have been messin' with me my whole life. I learned a long time ago that there's no sense gettin' all riled up every time a bunch of idiots give you a hard time. In the end, the universe tends to unfold as it should. Plus, I have a really large penis. That keeps me happy.
In the film Airheads, three slackers have taken a radio station hostage in order to get their song played. When talking to one of the DJ's to get him to play the song, the (black) man snaps, "Would you step back, please? You're standing on my dick."
This one joke forms the basis of an entire sketch in Movie 43.
Near the end of Requiem for a Dream, Marion seeks out drugs to satisfy her addiction and encounters a black pimp, who makes out with her and forces her to perform fellatio on him. Marion's hesitation prompts this comment:
I know it's pretty, baby, but I didn't take it out for air.
Nymphomaniac: Teased with but in the end averted. Joe goes so far as finding an interpreter so she can have sex with an African immigrant who doesn't speak a word of English. However, she doesn't do this because of the man's supposed penis size but because she finds the thought of not being able to communicate with her sex partner enticing.
A man goes in to get a penis transplant. The doctor opens up a drawer of four-inch penises, and the man asks if there is anything bigger. The doctor opens up a drawer of six-inch penises, and again the man asks if there is anything bigger. The doctor opens up a drawer of eight-inch penises, and the man shyly asks if there is anything bigger. The doctor responds "Not in white, sir."
Deconstructed in the novel The 13th Warrior, in which every culture apparently has this myth about one ethnic group or another. The Nordic women encountered by the Arabic narrator assume he'll be massively endowed; being well-traveled, he remarks that he's heard identical rumors in most countries, usually about a population that lives far away from whoever is spreading the rumor.
Becomes a minor plot point in Sirens where Ash is coming onto the black cop Ryan. Ryan is quite upset about this stereotype. He says that yeah, while some black guys play up this angle it's still insulting, and turns Ash down.
Of all places, The Golden Girls addresses this in an episode where Dorothy's youngest son gets engaged to an older black woman. Dorothy and co. meet up with her future in-laws and Sophia meekly asks "Is it...true what they say about black men in bed?" Before Dorothy can admonish her for it...
Dorothy then admonishes her mother for believing a stereotype, to which one of the in-laws replies, "Call it what you want, honey. I'm just glad it's true."
A plot point in the Curb Your Enthusiasm episode "The Surrogate", where Richard Lewis dates a black woman, and worries that he won't be able to satisfy her because of this trope. His friend, Larry asks a biracial woman about this, who tells him that there's no difference.
A Different World. While arguing with several white students from a rival college, Ron taunts them about Hillman's superiority in football and other sports, "but I'll leave out that physical endowment thing, since I know how sensitive y'all are."
Australian comedy series Full Frontal did a parody of a Levi's add in which a man has to hand over his jeans to bribe a Jamaican dockworker to let him stow away on a ship. In the parody the Jamacian isn't impressed with what he sees when the white guy takes off his pants, so unzips his own in response. Cue loud thump as the implied Biggus Dickus hits the ground.
Invoked and subverted in the first version of FATAL: There's a magical armor that turns you into a stereotypical black guy. Its very disgusting and racist effects include that "If the wearer is male, then those around him are 80% likely to believe that his manhood has increased, though it has not."
Gaijin Chronicles is the blog of a black man who teaches English in a Japanese middle school. The first post recounts his dealings with his students, whose only knowledge of America comes from television, specifically their enthusiastic assumption that he has a "bigu dikku" and desire to confirm the same.
The Dating Guy sort of invokes this. One episode has the gang going into the rainforest and coming across a black tribe in South America. Samantha, the girl, is to be wed to the man who has the largest penis; it's so large, it unrolls like a fire hose and the end cannot be seen. However, it never mentions whether Woody, the black guy, has a large penis or not. (He does get the most action out of the guys, though.)
Subverted twice in American Dad!, first in Finances With Wolves (Klaus's mind has been placed in the body of a black man, and he is shown browsing condoms — small, medium, large — before grabbing a garbage bag... which he fills with medium-sized condoms) then in Virtual In-Stanity (Dick's Digital Avatar is a huge black man, and at the end of the episode he is shown buying the smallest brand of condom available, while worrying that they may be too large).
Subverted again on The Simpsons. Marge has become wealthy and successful after opening up a women's gym, and Homer has heard from some other men there that these successful women will ditch him in favor of younger, more attractive men. Marge is talking with two other women at a business convention, and one of them suggests getting "a big black one." Homer fears the worst, but then it's revealed that they were talking about purses.
Played with in Family Guy, where Peter, Joe and Quagmire are in Washington D.C and are sightseeing for a while. Quagmire later says this:
Quagmire: Wow, those are all the monuments I read about in school! There's the Washington Monument *camera pans to the eponymous monument* And there's the Obama Monument. *camera pans to a larger, black version of the monument positioned right next to the Washington Monument*.
Another time, after an abstinence-only group comes through and gets all of Meg's classmates to take a virginity pledge, they circumvent the rule by having ear-sex (don't think too hard about it.) While the evening news anchors are reporting this, they claim that the old-catchphrase has been changed to, "Once you go black, you go deaf."
The Animated Adaptation of Black Dynamite is even worse than the film. In the pilot, BD has a censor bar hanging down to his knees. A black pornstar appearing in a later episode has a 22 inch monster that can kick up wind when he spins it around.
Referring again to the "prowess" version: In Minoriteam, the bad guys trick black superhero Fasto into a room full of Asian hookers, sure that he'll be distracted for hours. But seconds later, he's pleasured them all into unconsciousness and is ready to resume fighting the bad guys. (He has super-speed, after all.)