Chapter 36: The Parting of the Ways

Simplified Chinese (Mandarin: China)
分道扬镳 Fēn-dào yáng-biāo	分道扬镳 fēn-dào yáng-biāo = 'go different ways, part company' (literally: 'divide' + 'road' + 'lift up' + 'bridle bit').	Parting of the Ways
Traditional Chinese (Mandarin: Taiwan)
分道揚鑣 Fēn-dào yáng-biāo	分道揚鑣 fēn-dào yáng-biāo = 'go different ways, part company' (literally: 'divide' + 'road' + 'lift up' + 'bridle bit').	Parting of the Ways
Japanese
決別 Ketsubetsu	決別 ketsubetsu = 'parting, separation, farewell'.	The Parting
Korean
덤블도어의 사람들 Deombeuldoeo-ui salam-deul		Dumbledore's People
Vietnamese (Chinese characters show etymology)
Ngã ba đường	ngã ba đường = 'fork in the road, junction' (đường = 'road').	The Fork in the Road
Mongolian (new)
Зам салсан нь Zam salsan n'	зам zam = 'road'. салах salakh = 'separate, part' (-сан -san past tense). нь n' = 'about' (makes the preceding sentence into a noun).	About Ways Parting

The parting of the ways between those who are ready to fight Lord Voldemort and those who are not.

How is 'parting of the ways' translated?

The Mainland and Taiwanese translators both hit upon the same translation, 分道揚鑣 (Trad.) / 分道扬镳 (Simpl.) fēn-dào yáng-biāo, a four-character Chinese expression that exactly describes 'the parting of the ways'. The meaning is, literally, to 'take different roads and lift up the bridle bit (as if to go)'. Chinese is full of similar short, snappy compounds from its rich literary tradition.
The Japanese translator uses 決別 ketsubetsu, a parting or farewell with the implication that there is little likelihood of meeting again. The original characters for this word are 訣別 ketsubetsu, still used in Chinese. Japanese character reforms after WWII proscribed the use of the character 訣 ketsu 'parting', leading to the substitution of 決 ketsu 'decisive, definite'.
The Vietnamese translator literally describes the 'parting of the ways' as a 'fork in the road' (ngã ba đường).
Mongolian uses a common structure found in titles of stories: a sentence (зам салсан zam salsan 'the ways parted') followed by the particle нь n', which was originally a reduced possessive pronoun meaning 'its, his, hers', but now serves to mark a topic ('about, on').

(Detailed notes on the chapter can be found at Harry Potter Lexicon)