As I sit and watch my 4 hours of anime every week, I have often wondered why I enjoy watching what many consider cartoons? I do not think I have ever sat in front of a screen for longer than an hour, except maybe when I was a kid during Saturday morning cartoons. Of course, I was pretty young then. I think my enjoyment stems from two points.
First, I think the art and the animation are tremendous. The detail that a lot of the anime have is by far better than most TV or movie animations that you see in the United States. The animation quality is also better because of the more fluid motion. The characters seem to move in more life-like motions because of the complexity of the motion and the speed at which it is done. Often, the quality of the art is what most strikingly grabs you.
The stories of anime also appeal to me. I personally enjoy reading and watching sci-fi and fantasy stories which often are not done as animated movies or shows. Though not all of anime is sci-fi or fantasy, there is certainly more of it than on TV. The quality is also better not only because it is well written, but also well executed. For instance, Arislan is truly well done, where the magic is not over-used and the political power struggle between the various factions is shown. One can see what drives each of the different sides to wage war against each other.
The combination of the art, animation, and sci-fi plot give the anime a more complex and exciting look that I have not seen. It is also the ambitious themes that anime tries to cover that have always intrigued me. It is because anime has such a different feel to it that makes it so appealing to me and will continue to keep me glued to my seat for a long time to come.