In Japan there is a long tradition of male homosexual behaviour - it was codified among the samurai - but, as with so many other things in Japan, this is generally known but not spoken of. Modern homosexual behaviour is, similarly, generally known but largely kept on the down-low as it is a man's familial duty to marry and have children. So I understand from my Japanese friends (who are all from Tokyo, so it may be quite different elsewhere in Japan).
Friends from (the Catholic parts of) the Philippines have told me that things are a bit similar to what sykray described for Thailand. There are traditional social categories for men who act like women and women who act like men, and it is understood that these people will have same-sex relationships (though that term really doesn't apply; English just doesn't have the correct terminology for their relationships).
People I know from the Czech Republic have said that it's the most western of the eastern European countries when it comes to civil rights and social acceptance of homosexuality. The cities are pretty accepting while the rural areas are not, as a general rule.
People I know from the Carribean have moved out because of how homophobic the cultures and governments are. I'm sure people who choose to stay don't think it's so bad, but I've heard some nasty stories - and saying "from the Carribean" is a huge generalization. I'm sure it's very different for gay people in , say, Cuba than it is in Jamaica.
I've known one gay person who moved from Pakistan; he said that society there is not at all accepting, though I've read that it's fairly easy to hide because public affection between the sexes is verboten and you often see same-sex couples walking around (who are ostensibly heterosexual).
That's more or less what I know personally. As far as civil rights go, here's a handy-dandy map (and one that travellers may want to check out before they go somewhere abroad).
http://upload.wikimedia.org/wikipedia/commons/d/d7/World_homosexuality_laws.png
Unfortunatley, it only lists criminal penalties and marriage rights - non-discrimination laws and trans rights are noticeably absent. It's my understanding that Costa Rica should be turning a darker shade of green in the next few years.
This map is a bit more comprehensive, but a bit more difficult to interpret.
http://ilga.org/map/LGBTI_rights.jpg