Are gaijin ever portrayed POSITIVELY in anime?

Question:

gaijin is japanese for foreigner. that is what they call us white people who visit japan.
in all of the animes i've seen portraying american tourists, they're always stereotyped as being, arrogant, dumb, and having big nose and small eyes. it kind of offends me, because i plan on going to japan someday and I don't want to be perceived that way.

Answer:

The first answerer has it right.
I grew up in the USA, and I had a friend from Taiwan, who was very sensitive to racism. He would always talk about how Americans "assume every Asian person can do Karate or Kung Fu, that they are all good at math, studious, like anime, etc, etc." If you watch just about any movie, TV show, or commercial before about 1998 the stereotypes are unbelievably bad. Especially by black comedians and TV shows. Blacks mercilessly make fun of other minority groups. Asians are the smallest group, and the most "foreign," so they are the butt of the joke more often than not.
Anyway, this Taiwanese guy, who had a slight accent, and was the only Asian at my school at the time, was always asked by the teacher to "say something in Chinese," or "Do you really eat cats?" (by the fvcking teacher!) this was like 1995 or so--15 years ago--I'm not talking about the 1950's here. (I live in the South, maybe California/West Coast is better, but probably not much)

In Japan it's the same--to white people and blacks, lthough blacks have it worse. And South Asians/Persians/Arabs--brown-skinned people too. I finally understood what my Taiwanese friend was talking about. There is no racism in the sense of 1950's Alabama, turn the firehose on black protesters, lynchings and KKK.
However there is that kind of ignorant "You are white so you _______" Or "Let's point when we see a white person and have a contest to see who can speak like a white person the best."

So yeah, there are assumptions, some bad--Americans are fat and loud and totally oblivious to other country's culture, and Americans always smile, and are too enthusiastic about everything. In fact many Japanese people go to English schools simply because they are quiet and morose by nature and want to feed off the enthusiasm of the English teacher. They actually say that too: "Genki wo morai ni iku." That's not so bad, but some people also make really stupid requests:
They want a blond woman to teach the class, they want a chick who is not fat to teach the class, they want a Canadian (because Canadian English is easiest to understand--Yes, English in Ontario is so much different from English in Wisconsin), and they get super-pissed when the teacher is Asian-American--even like a guy named "Joe Takayama" who can't speak Japanese and whose ancestors came to the USA in 1880. More American than I am. But he's "not gaijin enough," or "not a real gaijin."
Working in an eikaiwa school will teach you about the dark underbelly of "kokusaika" "internationalization." Japanese want pretty young gaijin to be circus clowns, or cute little ryuugakusei who make humorous language mistakes and work really hard at the local 7-11 but can't pronounce "Irrashaimase" correctly. A few eccentrics like me stay, but for the most part, they prefer you to go home after your expiration date---"Use before 2012" like a gallon of milk. Most people who stay become cynical--complaining at the gaijin bar-- or delusional--defending Japan no matter what on Internet message boards, and trying to impress gaijin and Japanese ladies with their encyclopedia-like knowledge of bonsai trees or something. (It doesn't work BTW)