Actually, if you record your voice, you will find that your spoken voice has a slight accent, while your "inner voice" (the one you use to compose emails) has no accent. This is because talking to yourself sounds different, due to the acoustics of your head and ears (or whatever).
I think the fact that Socal has become the defacto American accent via TV may be distracting you.
Wikipedia page about it:
It's sad because it's such a beautiful and rich language; the young folks doing the translation are doing it a great disservice diluting it in their rush for volume.
For Arabic; almost every Arab is a gray-beard language nazi! All traces of foreign influence are removed with urgent and great prejudice. Which is good.
People that think they have this accent or that someone else has this accent will often refer to it as "no accent". It's not an ethnocentric viewpoint. Now, I definitely think the average person is not aware of how distinctive their accent really is and mistakenly think they have a non-regional one. But I do think it exists.
Just to give an example off the top of my head: take Conan O'Brien. He's from Boston, went to college in Boston but does he have a Boston accent? Maybe you could pick it out of his voice, but the average person probably wouldn't and he certainly doesn't have a strong one.
I then spent 2 years in Boston. And now 2 years in Toronto. My accent is completely mangled and jumps all over the place (ie, I might sound vaguely North American, but I know that you there's a 'h' in 'herbs').
It's worth pointing out that whilst I often get ribbed for having no accent...
it was a light hearted comment :)
I find accents hard to pick up but fascinating. I can just about make out the accent differences between my (town-sized) city and the next one though as there is a specific inflection that differs.