Well, I feel a great deal of affinity for Japanese culture. Right now, my parents are living in Japan, and it is such an interesting country, - who else would be able to turn raw fish into a delicacy? Very interesting history That, and I tend to be and anime fan- I love the drawing style, it seems to capture human emotion much better than more realistic stuff, plus you can find many interesting ideas and themes that you just won’t find in the Western World.
Like tentacle porn. 
I have, at various times, been obsessed with Ireland, Scotland, England, Russia, India, Mexico and France.
At the moment, one bedroom is a shrine to Queen Victoria and the other to Colette. The Colette room used to have an American Western theme and before that it was based on India.
I have taste. I know that I’m not supposed to like theme rooms. I just can’t help myself.
German… am fluent in their language, love the way they make their cars, enjoy their beer (although I think the Belgians make beer better), respect their work culture, like how open they are to foreign cultures (their relationship with Turkish residents notwhithstanding), love how they party, miss Munich a lot!
Disclaimer: Plenty other cultures also have the attributes described above - I just haven’t been exposed enough to them.
Also, I would have said the same for Italy, except that too much is similar to my own Indian (not Hindu) culture, which according to the rules set out by the OP, disqualifies it from my list.
My ethnicity: Indian/Spanish
Greece, the UAE and Egypt are the other countries that absolutely fascinate me. The history behind them, languages, food and the people are all so attractive.
Total hi-jack:
You don’t have Christmas crackers there??!! But, but, but - what do you do after Christmas dinner? What does Grandad wear on his head when he falls asleep in his chair if not a silly paper hat?! What do the children have to fight over if not the cheap plastic novelties that for some reason are infinately more fascinating to them than the hundreds of pounds worth of presents they received only that morning?! What do you groan over if not the unbelievably ancient and corny jokes?! AMERICA, HOW DO YOU COPE??!
I’ve been obsessed by the northwest corner of Europe–Ireland, England, Scotland, Wales–for as long as I can remember. My grandfather had a grandparent from each of those countries, although he identified primarily as Irish Catholic.
I always find myself intrigued by what I think of as niche people: either cultures found in very harsh climates, like the aboriginal inhabitents of Greenland and eastern Siberia, or minority cultures which maintain their identity even though there may be great pressure to assimiliate or outright oppression: the Jews, the Ainu, the Rom. The more unknown the origins, the better; I could read about the Basques or American groups with mysterious beginnings like the Melungeons all day.
Finland. For a couple of reasons.
The real reasons: They seem to do a lot of good stuff there, computing wise. My theory is that the weather is so bad that nobody has anything better to do that sit inside and program. However, it’s led to Linux for one thing, and some quality games such as Triplane Turmoil, Pizza Worm, and Elastomania (I think these are all Finnish). Other than that, it also just seems like a cool place. I think I was most impressed by the fact that they somehow managed to democratically elect a female leader, which implies that there must be an astonishingly small amount of (for want of a better term) dickheads living there.
The other, significantly less genuine reasons: The Python song about Finland is great, and my name is Finn (not Isaac).
Finland, Finland, Finland. The country where I quite want to be…
Yeah, that’s basically it.
~ Isaac
I have affinity for Indian Hindus.
…and I love black people.
I don’t know if I’d say I feel an affinity for it or its culture, but America fascinates the hell out of me. I love it, and I’d love to go there. I guess I have to choose my cultural selection a little more carefully than others (I don’t get excited by South Park the way someone may get excited into Japan may get excited by anime), but there are things that satisfy my obsession. Indie Rock is a good place to look, as is indie film. But there’re also weird, insignificant things as well. Like the giant Wal-Marts. When I go to America, I’m going to seek out a giant Wal-Mart.
I think Japan is pretty cool too, but I’m not into it like I am America.
Last year, we had a visiting professor from Finland at my school, and during his first lecture, talking about himself and Finland, he said: “If you were to ask me what kind of place Finland is, I’d show you this picture.” He then produced a page from a Finnish magazine. On the photograph were two men who looked like they were in their fifties. They were outside, wearing nothing but bath towels around their waists. The professor then explained: “the man on the left is our prime-minister’s husband. The man on the right, is the opposition leader’s husband.”
I wish I could have been born a rich, upper-class Grecian female at the time of Sophocles 
Too bad they don’t have a lot of information on the day-to-day life. I mean, they do a lot with what they’ve got, but I want to know how exactly they made their food, how they spoke, how they worshipped.
I will learn ancient Greek some day. I will buy tons of books in Greek and have entire bookcases sagging with their weight.
Strangely enough, I don’t want to go to Greece!
jovan: Ah, excellent - thanks for telling me that. Finland is clearly the place to be. But then, maybe I’m biased - if I saw two opposing political figures (or their spouses, but particularly if they’re male) in that situation and they were from somewhere else, I’d probably be suspicious. 
~ Isaac
Another Russophile here. However, I actually converted to Russian Orthodoxy and am pursuing a degree in Russian studies, with the eventual aim to move to Russia.
Oh, yes, and I wish I could have been a rich, upper-class female during Prinny I just love the outfits.
Jennyrosity: Yes, we have Christmas crachers here; but nobody knows about them. You pretty much have to go to an English/Irish/Scottish import shop to get them. I get mine from England via the Internet.
I talked the company from which I was recently made redundant into having crackers at last year’s holiday party, but I was travelling at the time and missed out. (They did save one for me, which I popped at my desk. And before I left on my holiday I passed a few of my own around to some co-workers at lunch.) The VP’s administrative assistant was born in England, so she thought it was a great idea – especially since my former company is owned by the large British conglomerate GUS. I heard that the people at the holiday party really enjoyed them and thought they were great – once it was explained to them what they were and what to do with them.
I started a thread last year when my crackers arrived.
Correction: The “VP” was actually the president of the department.
Mine is Mexico, and American Latino culture. My husband is from San Diego and thinks I’m completely bizarre for it, so I keep it to myself. He, otoh, loves all things British* and Japanese.
*And funnily enough, that’s what I am.
Cultures that fascinate me?
Japanese (though I am by no means an over-the-top anime fan or anything…)
Chinese.
All Scandinavian, but especially Icelandic and Finnish.
Eastern European, especially Slovenian and the Baltics.
It is not a coicidence that all these cultures have beautiful women. They were the lure, but they’re not the reason I stick around.
Japanese for me, but the more I research it, the more I find it to be just as fucked up or more so than my own.
Of course it’s fucked up, it’s made up of people.
JohnnyL.A., my family always gets our Christmas crackers from Cost Plus. What’s the advantage of having them shipped all the way from England?
And no, I’m not you.