Other than anime series, there are also anime movies, which are usually excellent, and though animated, sometimes not really for children. You've probably seen anime movies by Studio Ghibli, which is distributed by Walt Disney in the U.S. (and in English). However, there are many other great anime movies that are not created by Studio Ghibli (although the ones created by them are also pretty good).
Anyway, here's a list of my top 10 anime movies (including a few non-Studio Ghibli ones), in no particular order, in case you want to start getting into the whole anime thing but don't know where to start.
So, there you have it. There's something here for everyone, whether you like sci-fi, drama, fantasy, or just like watching cute and cuddly, supernatural creatures. Happy viewing!