I used to hear this greeting several times a day when in Singapore.
In other English-speaking countries, is this idiomatic expression known, do people consider it funny, or just a terrible misconception of English?
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"Long time no see" is used in the UK.
It is informal. I do not know how widespread its use is but I expect people of most UK social groups and of most UK regions would recognise and understand it even if it was not a form of greeting they would use themselves.
It's common in Japanese (ohisashiburi da ne). Standard in US English. Most likely a feature in most languages.
In English it's also a trope, so that you can play off "long time, no _ " in a variety of other contexts.
It is common and informal in AmE. It is idiomatic (i.e. pedantically agrammatic but common enough not to sound 'off').
I have heard that it is a direct loan-translation of Mandarin 'hao jiu bu jian'.
In common use in Ireland as well.
As for etymology, I'll put forward that is has a comma and comes from USA and specifically from Western films, where you'd oft here an american indian would say "long time, no see".
I agree with n0nChun that it is very common in India. The reason could be that most of the Indian languages have an equivalent that would roughly translate to long time no see
Um, I'm Indian, and most of the guys of my generation here, have caught up to it!