At its most general, Japan and the West (especially America) have wildly divergent ideas about gender and what is appropriate to show children on television. As a result, series marketed based on age will usually skew slightly older outside Japan, sometimes even breaking a Fleeting Demographic Rule. This is most noticeable with shonen series. In addition, Japan's strictly-defined gender roles do not exist to nearly the same extent in the West, thus it is much more common for series aimed narrowly in Japan to have Multiple Demographic Appeal in America and/or Europe.
Several anime series in general that in Japan are targeted at children often have teenage or adult fanbases in the West. A lot of series (even shonen) usually have comprehensive storylines, aren't afraid to show violence on-screen, or feature themes that're rarely seen. In the west, this is normally associated with what's targeted at older people, and in part was what helped people decide to give the middle finger to the Animation Age Ghetto.
This usually applies to every anime and manga that falls into the seinen demographic that isn't something like Black Lagoon or Berserk (though see more on the latter below). Series like Chobits, K-On, and CLANNAD are officially marketed to older men, but the majority of their fandoms seem to be made up of younger people.
Many seinen series are popular among female fans because of their greater focus on Character Development and similarity to shoujo in some series.
Key Visual Arts games/anime tend to invoke this, but Little Busters deserves special note: despite being very clearly Seinen with both clean and not-so-clean game versions, it has become popular enough with players who aren't straight guys that there exists official merchandise of a Kyousuke 'hugging pillow'. Or maybe that's just Kyousuke.
A surprising amount of crossover audience occurs between Moe and Shoujo's demographics when they emulate each other. Shoujo series often do well among older male audiences, and many shows from Sailor Moon to Futari wa Pretty Cure, are designed with Shōnen elements. Similarly, a reasonably cleanMoe show aimed at men, can do fairly well among fangirls looking for something different than the often romance-based selection of shoujo and who are attracted by the extremely cute designs. Case in point shows like Lucky Star and Manga/KON despite being aimed at males have very large female fanbases who are as attracted to the Moe element as male fans.
Moe fandom can also have a much larger subset of females outside of Japan. Part of this is because fansubbedshoujo series are much scarcer, and fansubs remove the broadcast time constraints of shows. A show that manages to keep its fanservice at a tolerable level while using female characters who avoid annoying shoujo tropes is very likely to draw in female fans.
Slice of Life in general have been meant for male Otaku in Japan, but also nowadays act as a means for Yuri and Shoujo Ai to exist on broadcast TV while maintaining some popularity. Stuff like Saki and So Ra No Wo To are good examples.
A lot of yaoi anime videos on YouTube - be it the actual series, AMVs, music, etc. - are most popular with females age 13-17, females age 18-24, and... males age 45-54.
Yaoi in general attracts bisexual or gay men. Some dislike it for its Unfortunate Implications and cheesiness, others like it precisely for the latter (God help those that like it for the former). And the Fanservice. And every now and then you may find the heterosexual man that reads Yaoi just because.
Some series fail to attract the originally targeted gender audience: Gensomaden Saiyuki failed so hard to attract a male audience that subsequent anime and manga series were switched from Shōnen to Josei, mostly due to the overwhelming amount of gay vibes. Likewise, Shonen Jump series Majin Tantei Nougami Neuro was fansubbed and scanslated in America with a very very low percentage of male fans. Other Shounen Jump series like Hunter × Hunter and Get Backers± technically, GB is from Kodansha's Weekly Shonen Magazine, not Shueisha's Weekly Shonen Jump, are split on gender attraction; the latter of the two acknowledges this, especially in the anime.
Male Slice Of Life is a strange thing, since even though it is Fujoshi bait, they often include female characters to keep the male viewers interested.
Idol anime for little girls are popular with adults. This is primarily because they have mature writing, decent music and cute character designs.
The bishounen cast of Gundam Wing was created specifically to attract female viewers, something mecha series typically lacked at the time. It worked and nowadays it's rare for a mecha series not to have bishounen in the main cast. As for Gundam, with the exception of ∀ Gundam every show since Wing followed the "pretty boys in mecha" formula.
Rose of Versailles has a substantial fanbase of men and older people who enjoy it for the drama of the 18th century and the charismatic Lady Oscar, though the original manga was aimed at teenage girls.
Sailor Moon, which was aimed at a young female demographic but had a large male fandom.
It still does, to the point where Hot Topic is selling male-specific Sailor Moon t-shirts.
In another strange example, the "main target" of Pretty Cure is said to be females ages 4-12... and males ages 16-35. It's telling that the director of the original series, Futari wa Pretty Cure, has Dragon Ball Z on his resume. There's also blatant Yuri subtext between the two main characters that would go over the heads of younger viewers.
This is especially noticeable in the 2010 Heartcatch Pretty Cure. Every episode has magical girl kung-fu fighting that rivals some Shounen fighting anime aired at the same time.
There are, some Periphery Demographic outside those demographics. According to Youtube, the viewership of the intros of the series has significant portion of men aged 35-55, way above what it was originally meant to. According to Website/Deviantart, large amount of fanart drawers for the series are adult women.
CLAMP's X1999 is a shoujo series, yet its themes of humanitarianism, environmentalism and dualism, as well as its heavy doses of action, violence, death and other dark themes makes it very often mistaken for shonen or even seinen, and is popular among boys as well as girls.
GaoGaiGar was the final entry of the Braves series by Sunrise, and as such, aimed at children. The show didn't do very well with the main demographic, but was a smash hit with the older otaku who had grown up with the likes of Getter Robo. The same happened in the U.S., where the fanbase is almost entirely adult mecha-lovers. Oddly enough, the sequel OVA series, Gao Gai Gar FINAL tried to bank on the older demographic with more fanservice and violence, and wasn't quite as well-received.
Cutey/ie Honey was a dyed-in-the-wool seinen superhero sci-fi series. The more tame TV series actually attracted younger female viewers, who by this time had equated her with their more familar Magical Girl, who themselves might have been inspired by her. Go Nagai admitted this side fandom surprised him, given the amount of racy humor is in the original work.
Because of this, there was a spinoff series called Cutey Honey Flash, made by the same staff as Sailor Moon, aimed directly at a female audience.
Cutey Honey has sort of became an icon of feminine beauty in Japan, appearing in advertisements for things like weight loss drinks.
Dragon Ball Z is an old Shonen anime involving Ki Attacks, aliens, evil space overlords, and the occasional dinosaur. It has gained a massive American fanbase of women and girls from the ages of 14-25. This probably has something to do with the huge bulging muscles.
One Piece is really, really popular with girls and women. It might have something to do with the ludicrously masculine male characters. According to this chart◊, there are more 50+ year old than people aged under 18 reading it.
May also have to do with One Piece being remarkably progressive, gender-wise, for a Shonen series. While there are still some Unfortunate Implications (Brook, we're looking at you!), the show compares very favorably to the many more sexist anime out there.
It probably also has something to do with how well constructed and worldly the whole story is. Sure the main character is somewhat childish, but the world around him is well formed and very rich with history, and the whole thing feels like it's headed to one hell of a finale, even if the story has only just reached the halfway point.
Hetalia is an odd case in that it started off as a webcomic, with no real demographic in mind. It's a Seinen manga by default, as it was picked up for serialization in the Seinen monthly magazine, Comic Birz.
The anime for K-On!, a moe series aimed at otaku, became so popular with young girls that it also airs on the Japanese Disney Channel, right alongside Hamtaro and Alice Academy.
Trigun (Shonen) and Trigun Maximum (Seinen) is very popular with fujoshi over in Japan. Most doujinshi, and fan art on Pixiv and artists' personal sites, are either yaoi or a "cute guys doing cute and funny things" type deal.
Rurouni Kenshin owes much of its success to female fans, despite being an often-violent action series published in an anthology aimed squarely at boys. The show's title character, a soft-spoken, gentle bishonen with a hidden, more violent dark side, most likely helped. The well-written romance between him and the female lead most likely helped too, especially since it was one of the few shonen manga relationships that had real development and a definite resolution, while most shonen couples get bogged down in an eternal game of "will they or won't they?".
When the Kenshin movie premiered in Japan, something like 2/3rds of ticket-buyers were female — which was roughly the exact opposite of the gender split for a Shonen Jump film at the time.
A fair number of guys like Fruits Basket. While they don't really care about the bishonen bunch, the story is well-structured enough for them to care, and its humor is pretty much universal. It doesn't hurt that the female characters are well developed, and cute to boot.
It's a good bet that most of the current YGO fanbase consists of fans of the Abridged Series.
Magical Girl Lyrical Nanoha is an interesting case, taking the usual Periphery Demographic for Magical Girl series (16-35 year old men) and creating the series to appeal to them specifically. Even so, there are quite a few younger girls who enjoy it. So the "normal" demographic for Magical Girl shows is the Periphery Demographic for this one? *head explodes*
Ranma 1/2 is a shonen series meaning it is supposed to be popular for teenage boys. In Japan, according to and surprising creator Rumiko Takahashi, it was more popular amongst girls than guys and Animerica in the year 2000 said that it increased the number of female readers in the American manga market.
Katekyo Hitman Reborn! is also a shonen series, but a fairly large minority of its readers are Yaoi Fangirls. The WAY too many bishounen characters in that series help, and yet it's adding more.
Well, you can't make a show about a teenage boy who spends most of the first season running around in his underwear without atracting at least some female fans.
Rebocon, a concert dedicated for this series if you watch the video you will only hear girl's screaming.
If you just look at the title of Maid Sama (Student Council President Is A Maid!), it sounds like a moe series aimed at the male otaku crowd. In fact, it's a shoujo series about the female student council president of a formerly all-boys school who has to work at a maid cafe to help her family put food on the table and attracts the attention of the school's resident bishounen. This doesn't stop guys from watching it, though. The series' equal focus on romance and wacky humor, not to mention the attractive female lead and likeable male lead, attract plenty of male fans.
Starting from about the same time as the Genre Shift, Ken Akamatsu, the creator, began adding little hints of Ho Yay to the series. Whether this was a result of the Periphery Demographic or the cause of it is extremely debatable.
Princess Tutu is about as girly as a shojo can get, but has nonetheless developed an adult male following that heralds it as an metafictional epic whose awesomeness can only be compared to ninjas engaged in a rock battle — Hence it's Fan Nickname: Guitar Ninjas.
Victorian Romance Emma is, rather surprisingly, a seinen series, but it enjoys attention from all the other demographics. A great deal of the interest in the show is in the fact that it's a show about a maid, but it's not a Meido show.
Maria-sama ga Miteru was initially aimed at teenage girls, what's with its melodramatic story and dreamy atmosphere. But since it's Yuri, it has strong male fanbase. The author herself have satirized this phenomenon many times in the story.
This even crosses into Multiple Demographic Appeal, as evident with the OVA release. The ending was performed by KOTOKO, who is known for performing opening and ending of Eroge aimed at men.
Hamtaro is a Kodomomuke series but it still has a significant teenage and adult female fanbase.
Nobuyuki Fukumoto, who writes series geared at adult men with a rather unusual artstyle, has a surprisingly big female fanbase. This may be due to the infamous lack of female characters in his work, which provides fodder for Yaoi Fangirls. And, of course, KaijiisMoe.
Viz recently mentioned that Tiger & Bunny is intended for 14-25-year old males. This brought on many laughs from the rather large, veryfemale fandom that's formed around it.
Still on Pixiv, Nintama Rantarou, of all anime, also has its own separate tag for exactly the same reason. You'd never guess that from the content of the anime, which is day to day adventure of a band of goofy ninja kids. Maybe it's the women who watched it in their childhood.
Pani Poni Dash! was quite popular for children, despite aiming for the more cultural audience to get the pop culture reference. It does help how crazy and all over the place the anime is, though, which would guarantee tons of laughs.
Kanamemo has it's share of female fans appreciating the yuri context for the sake of cuteness.
Ouran High School Host Club, despite being a bishonen-ridden reverse-harem series, is well-written and hilarious enough to attract a sizeable male audience as well. Another appealing aspect is that the female protagonist is a cute but sensible girl who's refreshingly more realistic than most shoujo heroines and how much focus and development is given on the host club members.
Pokémon Special is published in magazines aimed for elementary school kids, but its strong sense of character and continuity draws in older readers, especially those nostalgic for the games but got tired of the anime.
This also applies to the Pokémon anime itself, although to a lesser extent than the games and (possibly) the manga. This may be because unlike the games and manga, the anime's writers very rarely cater to the Periphery Demographic itself. Despite this, nostalgia for the early seasons of the anime tends to be very strong (partly due to Pop Cultural Osmosis), and many people just enjoy the anime for what it is.
Bakugan is a typical Merchandise-Driven Mons anime, generally aimed at 6-11-year-old boys. The character designs of the humans, both male and female attract teenagers and 20-somethings who could care less about the story. There are also all manner of adults who buy the figures and cards and have long discussions about the mechanics of the game.
Even Berserk has a much larger female audience than you would logically expect from its well-earned fame as one of the goriest, most disturbing stories in existence. This is because its female characters are non-stereotypical, not to mention that it is perhaps one of the few works of fiction that treats rape and its psychological repercusions with realism and, what do you know, respect. And that, as fans will quickly tell you, the main story is based on more universal and epic themes than "tits and gore", infamy be dammed.
Fairy Tail: Another case of a male-targeted shonen series that females fell in love with. Natsu's chest is on full display under his vest, and Gray Fullbuster has as many female fans in real life as he does in-universe. It's to be expected when one has a habit of stripping down to his boxers (albeit unwittingly). There are strong female leads in Lucy and Erza as well; though a fair number of women also happen to be fantasy fans.
MÄR, the anime anyway, got hit with this pretty hard. The manga is a relatively gory shonen, aimed at an 11-16 male audience, the anime toned down the violence to make it more suitable for children, so it was probably aiming for a 9-14 gender-neutral audience, however the anime also ramped up the Fanservice, but only really in terms of Yuri and Yaoi fanservice, which attracted a HUGE audience of Yaoi fans that pretty much overtook the fandom. The show's biggest broken bases are all caused by what the Yaoi fans liked or didn't like and what everyone else liked or didn't like. Poor Snow has become The Scrappy to many for being caught in the middle. (As she's the only girl NOT exploited for fanservice but whose emotional connection to the protagonist interferes with possible Yaoi pairings).
Free! or "Swimming Anime" was originally only a 30-second commercial featuring school boys on a swim team. Naturally, fujoshi picked it up immediately and caused tumblr to explode. The news of it becoming a reality in July caused multiple fangasms. Though, it is popular with men too albeit to less an extreme sense.
Of course, Kyo Ani doesn't ignore the male fanbase as well as it tosses in Matsuoka Gou.