Chapter 16: The Goblet of Fire

Simplified Chinese (Mandarin: China)
火焰杯 Huǒyàn-bēi	火焰 huǒyàn = 'flame'. 杯 bēi = 'cup'.	The Flame Cup
Traditional Chinese (Mandarin: Taiwan)
『火盃』 "Huǒ-bēi"	火 huǒ = 'fire'. 盃 bēi = 'cup'.	The Fire Cup
Japanese
炎のゴブレット Honō no goburetto	炎 honō = 'flame'. の no = connecting particle ゴブレット goburetto (from English 'goblet') = 'goblet'.	The Goblet of Flame
Korean
불의 잔 Bul-ui jan		The Cup of Fire
Vietnamese (Chinese characters show etymology)
Chiếc cốc lửa	chiếc = counter/classifier cốc = 'glass, tumbler'. lửa = 'fire'.	The Fire Cup
Mongolian (new)
Галт цом Galt tsom	галт galt = 'fire + with'. цом tsom = 'drinking cup, goblet'.	The Goblet with Fire

Goblet

A goblet is a type of cup with a stem and a base. The object and the word both have an archaic feeling in English.

The Chinese-language versions (Mainland and Taiwan) use the word 杯 or 盃 bēi, a broad term for any kind of cup or glass.
The Vietnamese version uses the word cốc, which commonly refers to a cup (with a handle) or a tumbler (ordinary glass without a stem).
The Japanese uses the English loanword ゴブレット goburetto. This removes it from the ordinary class of everyday containers in Japanese.
The Mongolian uses the word цом tsom, referring to a drinking cup or goblet. It is also the term used for a cup as a sports trophy.

Fire

'Of fire' in English could refer to a goblet containing a fire, or a goblet made of fire.

The Japanese version uses the word 炎 honō, a slightly elevated word meaning 'flame'. The particle の no connects 'goblet' and 'fire'. The meaning is vague as in English.
The word for 'fire' in the Mainland Chinese version is 火焰 huǒyàn 'flame' and in the Taiwan Chinese version the simple word 火 huǒ 'fire'.

The Vietnamese translation uses the plain word lửa 'fire'.

The two Chinese-language versions and the Vietnamese version juxtapose the two words 'cup' and 'fire'. In the Chinese this is 火焰杯 huǒyàn-bēi 'flame cup' (Mainland) and 火盃 huǒbēi 'fire cup' (Taiwan). The Vietnamese is cốc lửa, where lửa 'fire' modifies cốc 'cup' using an order the opposite of English and Chinese.
The Mongolian uses the word галт galt, where гал gal is 'fire' and -т -t is a suffix meaning 'with' or 'having'. The Mongolian thus means 'cup with fire', which is more specific than the English.

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