In Japan 1/3rd of all printed materials are manga, and because of this you can find a huge variety of stories and genres
The Genre's and terms of Manga/Anime:
Manga: In Japan this term refers to any comic book whether it is produced in Japan or the U.S. , however for convenience for the rest of the thread I will us the general english definition of the world which is used to refer to Japanese cartoons.
Manwha: Comics produced in Korea. There are a couple of good ones out there, although not quite the same number as Japan. They can mainly be distinguished by the fact that they usually have far more assertive and strongwilled female characters and their drawing styles tend to be far less cartoony than mainstream Japanese or American comics.
Shoujo: Mainly romance stories aimed at younger teen girls between the ages of 8-14.
Shonen:
You know all those action manga that everyone knows about. DBZ, Naruto, Bleach, etc? That would be this category. Ever wondered why those plotlines seemed so simple and repetitive? That's because the target audience is 8-14 year old males.
Seinen:Manga aimed at male readers between the ages of 18-30, this genre tends to have the best plots of most manga and is the most widely read by adults in Japan.
Josei: Manga aimed at females readers between the ages of 18-30. They tend to be romances, but with more developed plots and characters.
Be Careful of:
Yaoi/Shonen Ai: This genre can basically be summed up as guy on guy.
Hentai: Basically cartoon porn.
Yuri: Lesbian manga