Oh my, lots and lots. Ginger has possibly the most ramified etymology known. I can't do this properly without tree diagrams, and I think they need to be three-dimensional too, so accept this list as a poor substitute.

Modern and Middle English: ginger
-- which gave
Middle Irish: sinnsar
Modern Irish: gingsear
Scots Gaelic: dinnsear
Welsh: sinsir
-- and came from
Old French: gimgebre
-- which also gave
Modern French: gingembre
Old High German: gingibero, gingiber, inguber
Middle High German: gingebere, ingeber, ingewer
Modern German: ingwer, dialectally ginfer, imber
Middle Low German: gingeber, ingever
Plattdeutsch: gemware, engeber
Middle Dutch: gengber
Modern Dutch: gember
Frisian: gingber-wirtel
-- and one of the High German ones gave
Russian: inbir'
Ukrainian: imber
Polish: imbier, imbir
Lithuanian: imberas
Latvian: ingvers
Estonian: ingver
Slovene: imber
-- while one of the Low German ones gave
Swedish: ingefära
Finnish: inkivääri
Danish: ingefær
Icelandic: ingifer

Back to the Old French. That came from
Latin: zingiberi, zingiber
-- which was also borrowed as
Italian: zenzero
(-- giving Czech: zázvor)
Spanish: jengibre
Portuguese: gengivre
Occitan: gengibre
Catalan: gingibre
Hungarian: gyömbér
(-- giving Slovak: d'umbier
Serbo-Croat: djumbir
Romanian: ghimber)
Old English: gingifer, gingifere -- note that the OE was discarded and the word reborrowed into ME (above) from MF

The Latin was from
Greek: zingíberis
-- which gives
Modern Greek: zengíveris

The Greek was from
Pali: singivera-

Let's bookmark the Pali for now, because we'll need to come back to it to trace further back. For now we confine ourselves to other descendants of the Pali. It gave
Sinhalese: inguru
Uyghur: singir
Malagasy: sakaviru
Armenian: sngrvel
Pahlavi: sngypyl
Sogdian: snkrpyl
From one such Middle Iranian language came
Aramaic: zanghebhil
-- whence
Syriac: zenîghber
Hebrew: zanghebhîl (the modern surname Zangwill)
Arabic: zanjabîl
-- and this like so many Arabic words spread far and wide as
Turkish: zencefil
Albanian: zenxhefill
Bulgarian: zhindzhifil
Modern Persian: zanjabil
Georgian: janjap'ili
Kabyle (a Berber language): skenjebbir
Swahili: tangawizi
Bondei (I presume this and the next three are African but I haven't heard of them): sangaizi
Taita: tangaisi
Kamba: tangaisi
Nika: tangaizi, tangawizi

Now back to the Pali, the Buddhist scriptural language descended from
Sanskrit: srngavera-
-- also giving
Prakrit: simgabera-
The first part of the Sanskrit has been influenced by srnga- 'horn', from the horny appearance of the rhizome. We must divide the word into two roots (ahem) at this point. The second half is a Dravidian element meaning 'root' (Tamil and Malayalam veer, Kannada beer, Tulu beeru, Telugu veeru), and need not concern us further. The first element is the part that actually meant 'ginger', evidenced as
Malayalam: inci, from *singi?
Tamil: inji
Sora: sing

At this point my source (A.S.C. Ross in Etymology, André Deutsch, 1958) says that the original Indian words came from South-East Asia, but it is no longer possible to track the exact route. The eastern Asian forms cited are, losing all the vital accents,
Burmese: khyan (pronounced jin)
Cambodian: khnyi
Chinese: kiang
Dimasa: ha-dzin
Garo: e'-tsin
Haka: ai-tin
Japanese: kiô (now -ga in compounds)
Khami: ko-sin
Khasi: s'in
Khyang: t'en, a-t'en
Lakher: ia-san
Lhota: -san
Lusei: sa-t'in
Manipuri: sin
Minbu: t'en
Moran: hai-ten
Palaung: shi-aung
Rawang: lun-zin
Rengma: ga-sen
Rong: hin
Shan: khin
Shendu: a-tsain
Thado: tin
Thai: khin
Tipura: hai-tsin
Vietnamese: gung