"American cartoons place characters in situations; anime places situations around characters...anime characters are not like fictional characters but more like fictional people; their actions stem directly from their personalities, and not just as a means to move the story's plot forward...we are made to sympathize with them, and not simply be entertained by them..."
I think the characters are part of the reason why anime interests so many people. They're more realistic than most animated (or non-animated) characters. They have flaws and they're more human. The situations are also something that people can relate to or want to be able to relate to. There are a lot of anime situations that deal with real life issues and themes, and people can find themselves in them.
Also, I believe that the variety of anime provides the opportunity for more people to like it. "There's an anime for everyone. If you don't like this, you just haven't seen the one for you yet." That's what my friends and I always say. And the artwork is detailed and beautiful, too.
(And don't you love that quote? It's one of my favorites. ^_^)