Okay it's like this.
Any genere has it's stereotypes, Anime at one time was "new" here in the West but right now we're learning that it's just as cliqued as anything else if you watch enough of it. Also because it's successful (people paying $20-$30 for a couple of episodes) it means that we're getting a ton of crud shoveled over here where imports/translations at one time had to be fairly selective.
There is also the whole racism aspect, keeping something "Japanese only" can be a major selling point in Japan especially if it's something that "stupid Westerners" want or would like. Or at least this is how a few of the translated periodicals I've seen over the years have come accross (though admittedly I have not checked any out recently).
Some of what is being talked about is pretty typical for science fiction and fantasy in general (which is how I got into it). The idea of the main character starting out weaker than everyone else, but then turning into uber-man for example is a stereotype. The whole "boy done well" schtick. From old classics like "The Belgariad" (David Eddings) to more current works "The Codex Alera" (John Butcher) you see this kind of thing, and while it's a stereotype it all depends on how well it's written. The problem is a lot of Anime is badly written, I mean just like novels there is like 50 tons of it, and not everything is going to be good.
Trying to do the "So corny it's cool" schtick is also very hard to do, and very few things can pull off the high camp. Anime tries to go for this vibe more than a lot of other generes, and when it fails, it tends to fail spectacular. The holy grail for this kind of thing is probably Star Wars and it's overacted "Luke, I am your father" (bad quote of it since that isn't exactly how it was said, but we all know the scene) thing from "The Empire Strikes Back". It was pure overacted cheeze, but the movie itself was enough where by that point you got so into it that it seemed awesome.
As far as Harem anime goes, well again it's a genere convention and it's something that has to be done right. A good example of western versions are the "Myth Adventures" and "Wanderings Of Wuntvor" series. Both of which are about low powered mages (both of whom become more powerful, albeit without quite realizing it) surrounded by babes who lust after them. There is more to them than that, but it's pretty much the fantasy stereotype of the whole "Tenchi Muyo" thing.
Honestly I think Anime does so well in the US because they took a lot of it FROM the US to begin with (a lot has been said and written about Japanese pop culture, pseudo-Americanism, and hating us for wanting to be us... I won't retread it). I wouldn't be at all surprised if a lot of the things you see now ARE inspired directly by some of the older American works. They are pretty good at putting differant spins on old ideas, and truthfully they routinely play around with ideas in video or comics (visual art) that you otherwise have to read about. D&D/Western RPG conventions are also you see frequently in various fantasy Anime as well including some things that can only be described as a homage (of sorts).
To use "Myth" as an example, something like "Tenchi" (despite Tenchi being science fiction and styled a bit differantly) is probably the closest thing your ever going to find to actually seeing it... except perhaps for some of the ultra-rate "Starblaze" Graphic Novels that Phil Foglio put out (and as much as I like Phil, I felt they were a mixed bag in comparison to the books).
At any rate, by this point, pretty much everything that can be done, has been done. It's largely about how well you do it. This is true of most generes. On the rare occasion when you see something fairly original it will be milked until it becomes a trite stereotype, and then you become interested in how well people can tell very similar kinds of stories rather than being wowed by the concepts themselves.
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