Anime can be a fair bit deeper and more involved than most Western cartoons. Some anime can be childish or irrelevant forms of escapism; shows such as Pokemon and Dragon Ball Z are meant more for immediate enjoyment, for example. There are, however, more than a few series that can go pretty deep, where the stigma of "animated shows are just cartoons" doesn't actually fit.

Full Metal Alchemist: Brotherhood is a good example of this, as it can be pretty philosophical and complex. So can other shows, such as Stein's Gate, and even the "cartoonish" One Piece.

A fair bit of Japanese culture is wrapped up in anime, and over there, it's not just something that's targeted at kids, or shows like The Simpsons or South Park that are just there for a cartoon comedy niche. Anime can get pretty serious fairly easily.