Shoujo (少女 meaning young girl) is a category of manga/anime marketed to girls, typically 8-18 years old. It is one of the four main categories of manga/anime along with shounen (for boys), seinen (for men), and josei (for women). Since the josei category is less known by name in Western fandom and virtually never translated (either professionally or by scanlators), it is not unusual for a josei series to be called shoujo.
In the 1970s, shounen ai (a style of manga featuring m/m relationships and aimed at girls) developed out of shoujo. In the modern day, BL (as the genre is currently known in Japan) is often considered a separate demographic, though some people still consider it a subset of shoujo.
Japanese comics, in a form we would more or less recognize as analogous to modern manga, got their start at the beginning of the 20th Century. Manga from this period were short strips that were published in children's magazines that also featured fiction and other content. These manga are primarily interesting to scholars rather than fans.
1950s & 60s
Shounen manga began to take off post-WWII with Osamu Tezuka, the "god of manga", leading the way. The shoujo that was written during this period is usually seen as being inferior and is mainly of historical rather than fannish interest. Most of the authors were men who worked on formulaic shoujo romance before graduating to shounen manga (their true interest).
In 1953, Tezuka himself started a series known as Ribon no Kishi or "Princess Knight", a lengthy story about a crossdressing princess reportedly inspired by the Takarazuka Revue. It is known for its long, continuing plotline and relatively high levels of action and violence for the time. Though it has never been widely available in English, it was and is hugely popular in many other languages and has had a massive effect on shoujo tastes both in Japan and abroad. Many female shoujo artists of the 1970s credit this single work with inspiring them to try their hand at manga.
Though most manga artists at this time were men, there were a few notable female artists, in particular Toshiko Ueda, Hideko Mizuno, Masako Watanabe, and Miyako Maki. These artists are most interesting to current shoujo fans for their influence on later female artists. Hideko Mizuno is particularly known among English-speaking fans for her manga Fire!, a story of bikers and rock and roll, which features the first male protagonist of a shoujo series as well as the first sex scene in shoujo. The series is frequently reprinted, but is out of print as of 2009. However, many of her other works have recently been reprinted. She is best known in Europe for the anime Honey Honey (an adaptation of her manga "Honey Honey no Suteki na Bouken"). Members of the Year 24 Group cite her as an influence along with Tezuka.
The 24nen-gumi (２４年組, literally: "year 24 group") are a group of female artists who revolutionized shoujo manga in the 1970s. They were among the first women to work professionally as manga artists, and prior to that time, most shoujo manga were written by men. Pre-1970s shoujo was mostly formulaic romances, but the members of the Year 24 Group worked on topics including gay romance, suicide, insanity, women's sexuality, and other boundary-pushing fare.
Their name comes from the fact that they were all born in or around the year Showa 24 (1949), and they are also often called the "Fabulous 49ers" in English. These names and the group designation were applied to them by outsiders, so there is no absolute definition of who the members are. The group is usually said to include, at the very least, "Yasuko Aoike, Moto Hagio, Riyoko Ikeda, Yumiko Ōshima, Keiko Takemiya, Toshie Kihara, Ryoko Yamagishi, Minori Kimura, Nanae Sasaya, and Mineko Yamada."
They have a small but devoted following in the English-speaking world, mostly due to the efforts of Matt Thorn, an academic who works on shoujo manga. However, many of these fans are surprised to find that all members of the group are still alive and most are still publishing. Only a few of their oldest and most famous titles are known in the West, usually through footnotes in books and articles on the history of manga.
In Japan, it is much more common for doujinshi circles and other fandom of that type to focus on more recent artists, but many professional shoujo artists cite this group as their inspiration (or cite women who cite them). People who read their work in the 1970s are often still passionate fans, especially middle-aged women who are not necessarily paricularly geeky or involved in the production of fanworks.
Their work is known for its psychological depth, complexity, treatment of female sexuality, and, in many cases, feminism.
From Eroica with Love
Rose of Versailles/Lady Oscar
The Rose of Versailles by Riyoko Ikeda is well known among English-speaking shoujo fans from references in books and articles. The manga and its anime adaptation are widely available in European languages, but not in English. The movies are less popular and the Takarazuka Revue production, while the most popular they have ever done, is virtually unknown.
A second group of shoujo manga artists a few years younger than the original Year 24 Group were also highly influential in Japan. Some of them were more directly involved in the early doujinshi movement. Post Year 24 Group member Yasuko Sakata and Akiko Hatsu (younger sister of group member Yukiko Kai) coined the term yaoi in approximately 1980. Their works are not well known among English-speakers.
In the modern day, it is rare to find male manga artists who primarily write shoujo. However, a few notable exceptions do exist, particularly among artists whose careers started in the 1970s. Mineo Maya is well known for his farcical shounen ai manga Patalliro!. Shinji Wada's many works about homicidally kickass heroines beating the snot out of yakuza are sadly unavailable in English, but some adaptations of Sukeban Deka ("Delinquent Girl Detective") do have a following.
Sailor Moon and magical girls
Shoujo fandom in the US and other Western countries owes its existence to Sailor Moon.The henshin (transformation) sequence and other aspects of the magical girl genre appear in many other works, most of them directly indebted to Sailor Moon. Unbeknownst to many anime fans, this genre was largely inspired by the TV show Bewitched.
One fan claims:
- The first magical girl anime was Sally the Witch, made in 1966. Sailor Moon was unique in that it combined the super sentai genre with the transforming magical girl genre. Many people credit Sailor Moon for revolutionizing and popularizing the magical girl genre.
- "Was Sailor Moon completely original? No. All it did was combine two popular genres, so it had to have borrowed ideas. Does that mean that Sailor Moon completely copies Sally the Witch? No. Sally the Witch and Sailor Moon are nothing alike. They're both magical girl anime, but that's where the similarity ends. (By the way, Sally the Witch isn't exactly the epitome of all originality either. It was inspired by the American sitcom, Bewitched.) 
Another fan provides a brief history of magical girls:
- The American sitcom, Bewitched was quite popular among young women in Japan during the 1960s. During the 60s, animation was starting to take off in Japan with such series as Astro Boy (Tetsuwan Atomu) and Gigantor (Tetsujin 28-gō). However, despite really popular, the flourishing anime market was aimed at young boys. So as not to neglect young girls, the creator of the Gigantor manga decided to follow in the footsteps of Bewitched by creating an animated series based around a witch, Sally the Witch. It should be noted that a witch in Japan isn’t necessarily evil. This is something that is common in the west but in Japan, a witch is simply a woman who uses magic for the benefit of others (much like in Bewitched). 
The Wikipedia article on Sally the Witch provides more information:
- The first manga series was drawn by Mitsuteru Yokoyama in 1966, and was, according to Yokoyama, inspired by the American sitcom, Bewitched (known in Japan as Oku-sama wa Majo, or "The Missus is a Witch"). The anime series was produced and aired from 1966 to 1968 in Japan by Toei Animation. Unlike Yokoyama's Tetsujin 28-go, the series never received a U.S. broadcast, but was aired in Italy (Sally la Maga), French-speaking Canada (Minifée), Poland (Sally Czarodziejka – the Polish version was based on the Italian version) and South America (Bolivia, Chile, Paraguay, Peru, as La princesa Sally). 
Shoujo as a Genre
In Japanese usage, shoujo is a target demographic rather than a genre. However, many series do share common themes and styles, particularly series from the same era or same magazine. Shoujo manga series chosen for adaptation to anime are often more similar than shoujo manga overall. Shoujo manga series chosen for translation into Western languages are often an even smaller subset of that already small pool. Therefore, in the English-speaking world it is both common and fairly accurate to refer to shoujo as a genre.
The "Genre" in Japan
Common styles of shoujo manga in Japan include series set at schools (whether slice of life or romance), magical girl series, historical series, romantic comedies, stories about aspiring ballerinas, artists, actresses, athletes, etc. and occult and horror series. Science fiction settings were fairly common in the 1970s and 80s but are less common today.
Certain shoujo authors and certain shoujo magazines commonly include gay side characters, subplots, or subtext. (In works considered BL in Japan, this would be the focus rather than an incidental part of the story.) This is uncommon in shounen and seinen, though some series with strong crossover appeal like Naruto do include some fanbait-y subtext.
Shoujo horror arguably reached its golden age in the 1980s and 90s, and is often far gorier and more... well... horrifying than the target demographic might suggest.
- In Japan, horror has always been a major division of comics for girls (which is in turn a major division of all comic releases). Currently, more traditional forms of girls’ horror seem to have largely given way to murder mysteries of a style all too familiar to Western audiences.
If there is an obvious difference between shounen and shoujo series overall, it is that shoujo tends to focus a bit more on psychology while shounen is a bit more literal. However, both can be gruesome and violent or sweet and fluffy. Both tend to feature most of the same genres, though perhaps in different ratios: Dragonball-style action series with endless leveling up and boss fight type battles are quite uncommon in shoujo; psychological horror is pretty much unheard of in shounen (though it does turn up in seinen). Fantasy set in Heian Japan is more common in shoujo, while D&D-inspired high fantasy is more common in shounen.
Josei and shoujo exist on more of a continuum than shounen and seinen do. The most obvious difference between the two is that only josei commonly features slice-of-life stories about 30-something women trying to juggle career and family in modern Japan. In most cases, mature shoujo series are indistinguishable from josei series.
Shoujo art is often a bit whispier and more elegant than shounen art and is less realistic than josei or seinen art, but of course this varies greatly by artist.
These are, at best, tendencies: the only truly distinct thing about shoujo as a whole (vs. shounen, seinen, and josei) is which magazines it runs in.
The Genre in English
Shoujo manga series translated into English are often magical girl series, other fantasy series, and school romance series.
Shounen, seinen, and josei series that feature romance, strong fantasy elements, or many female characters are often labeled "shoujo" in English. Sometimes, this is because fans or critics don't understand the Japanese usage, particularly in the case of female authors like Rumiko Takahashi who write for a male demographic, but it is also often due to conscious rebranding on the part of the English-language publishers.
Popular Shoujo Series
It is difficult to pick representative popular shoujo series since what is popular in Japan is often not what is popular (or even available) in the West. What was popular in the US in the early 1990s when few series were commercially translated and scanlation hadn't really taken off yet is often quite different from what is popular in English today. Manga series with popular anime adaptations are usually popular in Japan but may not be elsewhere.
- Princess Knight on Wikipedia.
- Shoujo manga History on Wikipedia
- From the Year 24 Group Wikipedia entry.
- From a note in the Akiko Hatsu Wikipedia article
- Panda-chan on a thread at Sailor Moon Forum (Accessed May 20, 2011)
- A Kind of Magic – Part 1 (Accessed May 20, 2011)
- Sall the Witch - Wikipedia (Accessed May 20, 2011)
- From the introduction to Girls' Horror Comics, accessed November 4th, 2009.