You can see seemingly endless characters in video games, manga, and anime sporting the 'do as well as pop groups like AKB48.
Originally, the twintail was called "futatsu-yui" (二つ結い), which loosely means "two braids" or "hair done up twice". As in the West, it's traditionally a hairstyle worn by young girls, and it has come to symbolize innocence.
During the 1960s in Japan, there were twintail characters like Akko-chan in Himitsu no Akko-chan. During the decades that followed, the hairstyle continued to appear in manga and anime. Things really came to a head in 1992, with some truly amazing twintails appearing in Sailor Moon. That same decade, Japanese popstars like Puffy embraced the twintail, taking it well beyond its schoolyard roots.
According to the Japan Twintail Association, there are three basic twintail styles. First, there's the "rabbit style" that Hatsune Miku sports, with the hair braided near the top of the head. Then, there's the "regular style", with the hair braided right above the area behind the ears. And finally, there's the "country style", with the hair braided below the ears. There are, of course, variations to these basic styles.
(However, if you are adhering to pure "twintail" orthodoxy, the "rabbit tail" style is most "correct".)
Besides promoting and fetishizing this hairstyle, the Japan Twintail Association runs photo spreads of models sporting the dual tails. If you are interested in seeing how just how much of a variety there can be, have a look in the above gallery, which also features a relation collaboration between the association and Lollipop Chainsaw. You can see how illustrator NekoshowguN's Lollipop character designs very much reflect current taste.
Japan Twintail Association [Official Site]