In which countries is that “long time no see” greeting common?

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?

"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.