For a steady 20 years at this point, the landscape of pop culture has had an influx of magical girl shows from Japan. Ranging from the classic Cutie Honey to newer shows like Go! Princess Precure! there's almost an unlimited amount of magical girl anime to pick from.
The first example we have of a magical girl series is Himitsu no Akko-chan, a manga from 1962 by Fujio Akatsuka. It revolves around a young girl who is granted special powers from a spirit living in a mirror she buried in her backyard after it broke. Stop laughing, I'm not making that up. The series was well received enough to get it's own anime, but most people I've spoken with do not regard it as the first true magical girl series, but rather a prototype.
The first true magical girl series was a 1966 anime inspired by both Bewitched and Mary Poppins, is Sally The Witch (above). Sally was a hit, and was revived a few more times after it's initial run. The show is about a magical princess sent to our world, who happens to let her magic shine in different ways. No one knows she's a witch until the last episode though. We can draw parallels to Bewitched in that sense as Samantha used her powers through the show, but other than her husband (and her family), no one knew she was a witch.
The magical witch is a common theme in most anime. Through the 70's we had other witch anime such as Chappie The Witch and Megu The Little Witch. The 70's world of anime also brought us a new kind of magical girl; Cutie Honey.
Honey wasn't the traditional magical girl. For starters the series was a "shonen" (boys) comic. Honey was also an android, so her powers weren't magical. But she still had the common magical girl staples; she was ultra feminine, could do almost anything, and she was also the first magical girl to get a transformation sequence. Honey is one of the most enduring characters of anime, and over the years each subsequent Honey series (manga or anime) falls more under the magical girl genre.
Most anime fans will recognize the magical girl shows of the 1980's. Magical Princess Minky Momo and Creamy Mami were staples of the early stages of American anime fandom (hellooooo tape trading!) despite being two different types of magical girls. Momo already had her powers, while Yu from Mami was granted her special powers (but only for a year), and has a strong Jem and the Holograms feel to it. To this day both series have a strong following, and you can easily find DVD's and merchandise for them. There was a lull in new magical girl anime in the late 80's and early 90's, as giant robots were dominating the anime landscape.
However that wouldn't last for long. In 1991, Naoko Takeuchi introduced a young sailor suited soldier named Sailor Moon. I'll save a super detailed history and walk through of the greatest anime ever created (you can fight me about that) for another time, but Sailor Moon brought the genre back to life, and made it an international thing. Sailor Moon was a hit, and made a lasting impression on modern pop culture. While Sailor Moon had a lost of firsts (I'll talk about that another time) they did have some themes pulled from other shows. The transformation sequence was pulled from Cutie Honey, and elements of Super Sentai (Power Rangers ) are also commonplace in Sailor Moon.
Of course the shows success spawned hundreds of new magical girl shows since. Wedding Peach is one of those shows, but many fans consider it a direct rip off of Sailor Moon. Magic Users Club, Fancy Lala, Magic Knight Rayearth, and Saint Tail all came after, and made the 1990's magical girl revolution a thing. The genre hasn't slowed up since 1991. Pretty Cure is a hugely successful magical girl franchise, while Madoka Magica took the magical girl and made it darker and significantly less joyful. Even the Power Puff Girls got the traditional magical girl anime treatment with Powerpuff Girls Z.
The future for the genre looks bright. New magical girl shows are coming out every year (multiple times a year), showing young women of each generation that girl power is nothing to sneeze at, and to always believe in yourself. Oh, and to buy as much tie in merchandise as possible.