Averted, oddly enough, in Samurai X: Trust and Betrayal, the 1999 four-part OVA to Rurouni Kenshin. Episode three treats us to a series of quick cuts between Tomoe clutching her stomach and splashes of blood against a black background. She then heads outside before we cut to the next scene.
One of the chapters of Bokura no Hentai has Akane begin to menstruate. She's less than happy at her changing body.
A plot point in Wandering Son. Takatsuki is transsexual and starting his period causes dysphoria. On a lesser note menstruation is depicted several times from varying female characters.
Aversion: Mentioned once or twice in The Slayers, as female spellcasters lose power "that time of the month". Given the length of the series, it's surprising it only comes up once or twice with Lina, the first time as a minor plot point. Presumably she is little affected most of the time, or maybe it only affects her and a small number of mages.
Triela's periods pop up a few times in Gunslinger Girl. In one scene she's complaining about them but the slightly younger Henrietta notes she herself can't get them due to having her ovaries removed due to her Conditioning, though it's implied to be related to her rapes prior to the story.
Played straight in ElfQuest for decades, until the original creators decided to take up the series again.
LothÝriel by JunoMagic, in chapter 12 "Preparations for the Journey", puts the idea that the elves of The Lord of the Rings never bleed during their periods. "They reabsorbed whatever they had done to get ready once a month to conceive a child." LothÝriel, the woman from Germany, does not have periods because her birth-control implant suppresses them.
Discussed in First Try Series for how an massively unprepared Sakura is going to go through a two-month training mission without feminine products.
The Baby-Sitters Club: It's plausible for a thirteen-year-old girl not to have started her period yet, which makes a reasonable justification for the trope, but it's decidedly less plausible that none of them would have started menstruating by that age. Presumably it's not mentioned because the target age range for the books was a bit younger than thirteen, and they didn't want to freak out the kids (or their parents).
The Saddle Club: Played straight. The three main characters are all girls age 12-13, but periods are never mentioned save once offhand, rather jarringly, when the 13 year old talks about a Southern Belle etiquette teacher she had who always called it "that time of the month".
The Hunger Games: There is never any mention of what the female tributes do if they get their period in the arena. Do sponsors send them tampons? While some girls are young enough to not get their period and some are no doubt too underweight, it's hard to believe that out of more than 900 female tributes over the duration of the Games, not a single one should have had their period. Male tributes receive some kind of treatment to stop them from growing beards in the arena, so it would be unsurprising if female tributes received something similar to stop their cycle — perhaps ratings have shown that female tributes menstruating wasn't very entertaining. This would be fortunate in the second book when Katniss is pretending to be pregnant — if she had suddenly gotten her period, and it would have been noticeable given the amount of time the tributes spend in little clothing, and the entire plan would have been scuppered.
Blink and you'll miss it (it's just one paragraph in a long book), but this trope is averted in Lovely Assistant by Geoph Essex, where Jenny specifically notes a recent (minor) pregnancy scare before coming to the conclusion that she probably can't even menstruate anymore, now that she's a reaper.
Petals On The Wind : Zig-zagged. The protagonist, Cathy, is malnourished after years of being kept in the attic. Understandably, her periods have stopped, although her brother Chris raped her during their imprisonment, so she may also be pregnant. During a dance audition (and a very memorable scene), the floodgates open.
One wonders exactly how the Doctor's female companions broach the subject whilst traveling with him. It must be pretty awkward for a young human woman to ask a centuries-old male Time Lord about pads. As it has never come up in the show, we still don't know how they handle that.
Played ridiculously straight on Full House, considering that there were three girls living in the house (as well as an adult woman at one point), at least one of whom (DJ) undoubtedly reached the age of menarche at some point in the show's tenure and Stephanie likely reached this age too.
LOST has several women of childbearing age on an island with no feminine supplies, and yet it's never brought up how they deal with it. One character mentions being late, and another suddenly knows she's not pregnant, but the implications are never explored.
Averted in Katawa Shoujo. At one point, Rin (who has no arms) is getting antsy and wants to find her friend Emi. She's being evasive as to why, but Hisao keeps pushing her for an answer, and she finally replies that she's on her period and needs some help with that, and that while she likes Hisao, she doesn't feel comfortable asking for his help with that particular problem. Hisao promptly shuts up.
Averted in Corpse Party when Ayumi gets her period without realizing it (you begin seeing a blood stain on the back of her skirt partway through the game). She's very embarrassed when Yoshiki notices and asks when she got hurt, but she can't think of any way to change or cover it up. No one else comments on it though (either they think it's from one of the numerous dead bodies, or they just have bigger problems).
The elven and drow races of Drowtales are physically different then humans and can't get periods, leading to a Crowning Moment of Funny when one of the human cast members gets one and one of the drow uses her own confused idea of what it is to explain it, with large failures.
Averted in Misfile, as Ash, originally a boy, winds up horrified when Emily points out that the current symptoms he/she is experiencing are occurring after a certain amount of time Ash has been a girl. From then on, Ash will occasionally bring up the subject when he/she is feeling particularly irate.
In My Little Pony: Friendship Is Magic, the acquisition of one's cutie mark serves as the pony equivalent of puberty... except we know that ponies reproduce sexually and thus also have to go through actual puberty. That particular aspect of growing up is never addressed onscreen, though - which is fortunate, given that the innocuous stand-in for a girl's first period inspired the creation of a local club built around trying to make it happen. Probably best just to leave it at that.
Horses don't menstruate, but they do experience "heat". It would have presumably been dealt with offscreen whenever Mrs Cake was supposed to be pregnant. Foaling takes 11 months.
Amazingly enough, Grossology doesn't mention this in any of the episodes, despite one of the Grossologists being in junior high school. Most likely, this is related to its keeping the TV-Y7 rating.