I'm one of those people ... I just set out to install support for Chinese, Kanji and Hangul then I checked all was well on the Wikipedia page and I noticed other unsupported languages. Khmer, Tibetan, Kannada, Myanmar, even Gothic!
I just had to fix all these, here's how:
Chinese, Kanji: ttf-arphic-ukai, ttf-sazanami-gothic
For the other Asian languages just search in Package Manager for:
khmer, tibetan, kannada, myanmar
...there should be only one obvious choice for each.
Then for Gothic ... damase
Now there's only one language on Wikipedia not rendering but I'm done. (If I plan a trip to south-west China I'll revisit.)
To check you efforts visit:
Just to add to Toolz' post, if you're unsure of what fonts you need for a language you can just install the metapackages such as: