Shōjo Manga

shōjo, shojo, or shoujo manga refers to manga marketed to a female audience roughly between the ages of 10 and 18. 

The name romanizes the Japanese (shōjo), literally: "little female". Shōjo manga covers many subjects in a variety of narrative and graphic styles, from historical drama to science fiction - often with a strong focus on human and romantic relationships and emotions. Strictly speaking, shōjo manga does not comprise a style or a genre per se, but rather indicates a target demographic. 

(definition taken from Wikipedia)

Shojo Beat, a shōjo manga magazine published by Viz Media in North America from 2005 to 2009.

Some of my favourite shoujo manga are: 

Absolute Boyfriend, Fruits Basket, Fushigi Yugi, Ouran Highschool Host Club, Tokyo Mew Mew (all of these manga have been made into Anime series except for Absolute Boyfriend, it has been made into a short Japanese drama live-action series called "Zettai Kareshi")