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The only problem I have ever had with a Japanese accent was once some kids on Hai Karate had learnt a bit and didn't sound very good.And that woman on that episode of Go-Onger.

But I think you should pronounce english words in Japanese as english words. You might aswell speak the language you know properly.

Correct. Hence why I said "Anglophonic" later on in the post. But I was responding to someone who said American-accented Japanese was good, so I had to start there.

In any case, I know Czech, Korean, Indian, and Chinese native speakers as well. The Czech did not know Japanese very well (he was a first-year student in Japan when I knew him), so I can't speak for his accent. Google informs me that Hindi is not a stress-accented language, but they sound in Japanese exactly as you'd expect them to sound due to any experience you may have with Hindi-accented English (largely due to Hindi phonology like the multitude of non-aspirated stops).

Korean is pitch accent like Japanese, and Koreans who speak Japanese sound a bit like they have a stuffy nose to me.

And every native Chinese (whether Mandarin or Cantonese) I know has very good Japanese already. Still an accent—but I can't really characterize it since it was much more slight than anyone else's.

Oh yeah, and let's not forget the stereotypical inability of an anglophone to get the Japanese らりるれろ correct! However, to me, that mistake is much more endearing than the application of stress accent to Japanese.

I think so, lol. I'm from Fukuoka prefecture.
In Tokyo, some people say "please speak Hakata dialect".
I say "それとっとっと？"