Anime are, by definition, cartoons.

Quote Originally Posted by The Almighty Dictionary
Cartoon: a film made by photographing a series of cartoon drawings to give the illusion of movement when projected in rapid sequence.
Personally, I see the difference in anime as opposed to American cartoons just the same as I see the difference in Japanese horror films as opposed to American horror films. Either way, to say that anime is not cartoons is incorrect, just as saying that Japanese horror movies are not horror movies.

DMKA is correct though, cartoons in America are typically targeted at children therefore usually containing material that is entertaining to children. In Japan, they are targeted at a much bigger audience, thus containing relative content.