The word anime is used in Japan to describe the animation in general. In the rest of the world, this word is used as a definition of the Japanese animation. 

Is common thinking that the animation is entertainment for children. This is false, specially when we are talking about anime. A lot of anime movies and shows are not made for children. They have a very complex story, besides sex scenes and violence. Anime is, then, not a mere entertainment. It is a true art that has been growing in the last years.

There are lots of topics that can be shown in an anime series. The Japanese production of animation is the biggest one in the world. The main genres and examples are:

Mecha-genre: It uses giant robots and spectacular machines. Some of them, like Mazinger Z or Ironman 28, are pure entertainment. Some others, like Neon Genesis Evangelion and Macross, are stories with a complex plot.

Drama: This genre is made to cause an impact in the audience. An example of it is Fushigi Yugi. 

Romantic comedy: The more popular genre. Some examples of it are: Ranma 1/2, Saber Marionette J, Nadia in the Seas of Wandering, Maison Ikoku and KareKano, this one with a complex analysis of the characters psyche. 

Middle Age Tales: This stories are developed in a middle age atmosphere. One rep[resentative example is Record of Lodoss Wars.

Science-fiction: Adventures in a futurist atmosphere. Ghost in the Shell, Mospeada, Macross, Akira, etc., are examples of it.

Martial Arts: Another big genre. It is found generally besides some other genre. Examples of it are Ranma 1/2, Rurouni Kenshin, Dragon Ball, Street Fighter and Ninja Scroll.