Want to make a Very Special Episode that no one has done before? Simple! Have a character angst about being uncircumcised. Naturally, this is Always Male, and is mostly restricted to Eagleland (but not exclusively). In Eagleland, characters who angst about this are typically (though not always) of backgrounds which are typically uncircumcised. Because circumcision is most common in Jewish and Muslim cultures and in the USA (and American cultural satellites such as South Korea and the Philippines), this trope is a prime cause of Values Dissonance.
In the typical circumcision angst story, a male character either sees his buddies in the locker room and wonders why he's different, or thinks that his difficulty in the bedroom is because of it. He may be circumcised by the end without any medical necessity, resulting in a Broken Aesop. Not that this hasn't been inverted.
This trope has been in decline in recent years, likely as American circumcision rates are also in decline. If anything, an inverse trope is starting to appear, where men from cultures that do circumcise suddenly find themselves in cultures that don't, and receive the requisite stares from their peers. Sort of the Spear Counterpart to A-Cup Angst, though the much more common counterpart is penis size angst.
A variation occurred during the filming of Monty Python's Life of Brian when Graham Chapman opens the shutters nude in front of a crowd of Tunisians, who audibly gasped (and in many cases, ran away) when he came out. This prompted Terry Jones to pull him aside and tell him that they could tell he wasn't Jewish, which prompted Graham to nonchalantly call for props to... er, hide it.
Occurs as a throwaway gag in Robin Hood: Men in Tights: Rabbi Tuckman (Mel Brooks) offers the procedure to the Merry Men, claiming that it will make them more popular with the ladies. When they find out that his method takes away much more than just the foreskin (and employs a miniature guillotine) they quickly decline.
In Bryce Courtenay's The Power of One, main character Peekay is bullied for, as well as being English, being circumcised. Apparently the Dutch kids hadn't seen a "hatless snake" before.
Nip/Tuck: Resident psychopath Matt tries to get his dad to cut him in the first episode, and when his dad says no, tries to do it himself with wine and cuticle scissors. It goes exactly how you think it does.
On the other hand, Northern Exposure had Joel, a Jewish doctor who would be performing the circumcision and always complains about being underpaid, talk Holling out of it.
An episode of Sex and the City had this happen to one of Miranda's boyfriends because she was was squicked by the idea of having sex with a man who is not circumcised. The bizarre outcome was that after getting circumcised, he broke up with Miranda because he felt that he had so much to give now sexually that it would be wasteful to limit himself by a steady relationship.
Seinfeld: An entire episode revolves around Jerry, George, and Elaine discussing their experiences with uncut penises. The two male leads are (at least partly) Jewish so they know about this. However, it hasn't happened to either of them. Kramer, though, is a radical anti-circ activist, and tries to scare recent parents with horror stories of what will happen if they do the procedure. He later tries to steal the baby to protect him, and he is later assigned as the baby’s new godfather due to his stark display of concern for the baby.
Occurred in ER, where Benton had an argument with the mother of his son whether he should be circumcised.
On Married... with Children, Al Bundy had a quite legitimately angsty incident relating to his circumcision: He was in the hospital for an accident, and his chart called for a "circular incision." As Al Bundy's luck would have it, though, the doctors misread the chart and gave him a circumcision. Naturally, an adult man who gets a circumcision he doesn't want or need (and presumably, he hadn't been circumcised as a baby) will not only be pissed off, but suffer many side effects that give him an objective reason for feeling this way.
On Scrubs a couple can't decide whether to have their baby circumcised. They ask Carla for her opinion, and she tells them that there's no medical reason for it one way or the other. This only sparks more argument between them.
An episode of Penn & Teller: Bullshit! criticizes infant circumcision as a painful surgery with no medical necessity. The duo also suggest that circumcision causes sexual damage. As Penn was born in 1955 and Teller in 1948, it can safely be assumed that both men were circumcised as infants. In a later episode, they admit they have.
An inverse example on Friends. Joey auditions for the role of an Italian immigrant in a movie that involves a tasteful nude scene with a Jewish girl. The character specifically points out that it's the first time she's ever with a man who isn't circumcised, so naturally the actor who portrays him can't be either. However, Joey is, but he stupidly says he isn't just to get a callback. Monica helps him fashion a substitute out of luncheon meat, and it all goes great until he gets to the callback...
Joey: "That's... never happened before."
In an episode of King of Queens where Arthur is in the hospital, he tells Carrie to make sure the doctors don't circumcise him.
In an episode of Cheers, Frasier Crane tries to prevent his newborn son, Frederick, from being circumcised.
In an episode of Chank Yankers, one of the characters calls a Rabbi saying he is fixing to convert to Judaism, and asks him questions about circumcision, the character proceeds to vomit after hearing what the Rabbi tells him.
Religion and Mythology
Maccabees insisted on a more radical circumcision to prevent Hellenized Jews from regrowing their foreskins.
Played with in The Bible. At first, all Jews were required to be circumcised, possibly causing some of the first real life (albeit short) cases of this trope in non-Hebrew converts. But once Christianity comes around, it averts the trope by saying that circumcision isn't required anymore to resolve disputes between Jewish Christians and Gentile Christians.
At least once it was exploited. When two of Jacob's sons Simeon and Levi were angry that a Stalker with a Crush prince had raped their sister and demanded her as his bride, they agreed to it only if all the men in the city agreed to be circumcised. They did, and for the next three days all the men were helpless, making them easy to defeat...
Subverted in Something Positive: Branwen is the one upset about her boyfriend Davan's circumcision, as she worries it means he gets less enjoyment from sex. Davan himself is dismissive. "Just because I don't have an extra flap of skin on my dick doesn't mean I don't like sex."
On The Venture Bros., they've dealt with this twice. In fact, the boys die frequently and are replaced by clones, so Hank has been circumcised at least twice.
One episode had Dean rejected by English twins when they learned he wasn't snipped, since they'd spent most of their lives in the jungle, with a bunch of mostly-naked savages running around for whom the procedure was part of the passage into manhood. Their reaction is as much "Oh god he's just a boy!" as it is "eeewwww."
On South Park, Kyle angsts about Ike's upcoming circumcision. Due to some miscommunication between the kids and adults, they get the impression that it means they'll chop off his wee-wee. When told that he had the procedure, Kyle denies it fiercely before it's explained that they're not going to cut it off, they're just going to snip it "so that it looks bigger". The boys decide that that's okay, and that they want to be circumcised too.
On Futurama, they did the Freud Was Right version: Bender's antenna has to be snipped so they can get satellite. The entire apartment complex can't get satellite. By the end of the episode, Bender's antenna was reattached, and they moved back in to good old Robot Arms, with Fry still in the closet.
Freud's entire castration anxiety theory is based on Jewish men angsting about being circumcised.
There's some controversy about the long term effects of circumcision. Medical studies have proven and disproven all sorts of drawbacks and benefits (which you can probably find elsewhere on the internet — this is not the place to discuss them), and it doesn't look like there's ever going to be a consensus either way. Needless to say, given we're talking about surgery often performed on babies and closely tied to religion, both sides have some very... passionate supporters.