So...here are some questions:
Guan then.
1. What accent do you speak in when you speak your native language? Don't tell me you don't have one, because everyone has an accent, even if it's the "standard" accent for the language in question.
I speak with a (sometimes very heavy) cockney accent.

2. Do you mispronounce words because of your accent? I'm not talking about simple variant pronunciation. I'm talking about the way people in Boston say the word "career" like "Korea" and "Korea" like "career" (or, for example, the way Billy Joel sings about "Brender & Eddie" in "Scenes from an Italian Restaurant" ).
ALL the time; whenever i try to say anything that i don't use in day to day conversation or that has a lot of syllables i'll clip each sound to death; ridiculous becomes ridculahs also i hardly ever sound my t's and r's except when they're the initial letter in a word.

3. Do you speak any other languages fluently enough to have a distinctive local accent in that language? For example, my Moscow accent, my friend's Parisian accent when he speaks French, etc.
Nope.

4. Are any of your accents "looked down" upon? (For example, Cockney or similar accents in England, Algerian accents in French, Caucasus accents in Russian, Long Island accents in American English, etc., etc., etc. )
Yeh, without a doubt in my own country, but with the success of the british gangsta' flick genre and especially guy ritchie's films a fair few foreign people greet my accent as something to be enjoyed than endured, especially in the U.S.A.

5. As long as we're speaking about accents, are there any foreign accents which, when you hear your native language spoken in, turn you on/sound pretty ?
Most dialects of spanish.

6. Are there any foreign accents which make your language sound awful?
Yeh, english can be quite guttural and so can german, so german's speaking engish can sound pretty rough, but to be fair the reverse is probably true as well.
Okay, that's it. 'Twas a short survey.
not baaaaad.