I think the main reason it's so popular is it bridges the gap between TV for male children and male adults. What is there really for male teens? Not much. Look at the subject of most anime and it's stuff that appeals to young males (regardless of culture): action and boobs.
Not all anime is like that though. There's obviously stuff for girls considering the large female fan base anime has in America. At the same time, there's some really great shows/movies that can butt heads with any of the greats of American TV and cinema. Cowboy Bebop is a masterpiece among masterpieces. Planetes, Bakemonogatari, and ToraDora are incredible examples of story telling within their genres.
5 CM Per Second deserves its spot among with the great pieces of cinema. It's both beautiful to look at and a sophisticated examination of the way people grow apart through life. Grave of the Fireflies is just as powerful as any other war movie. Studio Ghibli has been recognized globally many times over. I could go on. Point is, there's great stuff to watch coming out of Japan. Calling any one culture the best is stupid, I agree, but being able to appreciate stuff from all over the world is a good thing, I'm sure you'll agree.
In regards to subs vs. dubs, anyone who speaks multiple languages can tell you that it's impossible to properly convey meaning across language. Sure, you can get the gist of things, but there are expressions, concepts, etc. that are entirely foreign to someone not familiar with the language and culture. For example, the word bishounen describes an incredibly attractive young man, usually slender and tall. The closest concept in English is a pretty boy, but the two words aren't really the same at all. Bishounen has a positive connotation. It's not a bad thing to be a bishounen, whereas pretty boys have this perception of only being good for their looks (i.e. they have no other redeeming qualities). The meaning of the word bishounen is completely lost in translation. THAT is why I watch subs any time I watch something foreign (Japanese, Spanish, French, German, etc.).