I believe this is on the self-explanatory side given the time at hand.

Afrikaans: Gelukkige Nuwejaar!
Alsatian: E glëckliches / güets nëies Johr
Danish: Godt nytår
Dutch: Gelukkig nieuwjaar
English: Happy new year!
Faroese: Gleðiligt nýggjár / Gott nýtt ár
Frisian: lokkich nijjier
German: Frohes Neues [Jahr] / Pros[i]t Neujahr
Icelandic: Icelandic: Farsælt komandi ár!

Jamtlandic: Gott nýár!
Norwegian (Bokmål): Godt nytt år
Swedish: Gott nytt år! Gott nyår!

Yiddish: Tov rosh!

Aragonese: Goyosa Añada Nueba!
Asturian: Feliz Añu Nuevu!
Catalan: Bon any nou
French: Bonne année
Italian: Felice anno nuovo!
Languedocian: Bona annada
Latin: Felix sit annus novus
Portuguese: Feliz ano novo
Provençal (Rhodanian): Bona annada
Romanian: Un an nou fericit!
Spanish: Feliz año nuevo / ¡Próspero año nuevo!
Walloon: Bone annéye

Belarusian: Шчасьлівага Новага году / Ščaślivaha Novaha hodu
Bulgarian: Честита нова година!
Croatian: Sretna nova godina
Polish: Szczęśliwego Nowego Roku
Russian: С новым годом! (C novym godom)
Serbian: Срећна нова година
Slovak: Šťastný nový rok
Ukrainian: З Новим роком

Latvian: laimīgu jauno gadu
Lithuanian: laimingų naujųjų metų

Breton: Bloavezh mat
Scots Gaelic: Bliadhna Mhath Ùr!
Irish: Athbhliain faoi mhaise duit

Greek: Καλή χρονιά / Ευτυχισμένο το νέο έτος

Estonian: Head uut aastat!
Finnish: Hyvää uutta vuotta!
Hungarian: Boldog új évet!

Turkish: Yeni yılın(ız) kutlu olsun / İyi yıllar

Aklanon: Mahigugmaon nga Bag-ong Dag-on!
Bikol: Mamura-way na Ba-gong Taon!
Cebuano: Mabungahong Bag-ong Tuig!
Hiligaynon: Mahamungayaon nga Bag-ong Tuig!
Ilokano: Narang-ay a Baro a Tawen!
Kapampangan: Masaplalang Bayung Banwa!
Pangasinan: Maaligwas ya Balon Taon!
Tagalog: Manigong Bagong Taon!
Tausug: Makasi Tahun Ba’gu!
Waray-Waray: Mainuswagon nga Bag-o nga Tuig!

Malgache: Arahaba tratry ny taona

Hawaiian: Hau’oli Makahiki Hou
Tongan: Monū’ia ‘a e ta’u fo’oú

Arabic:كل عام وأنت بخير
Berber: Asgwas amegas
Hebrew: שנה טובה

Korean: 새해에 복 많이 받으세요!

Japanese: 開けまして/新年 おめでとうございます

Chinese (simplified): 新年快乐!
Chinese (traditional): 新年快樂!
– Cantonese: San Nin Faai Lok!
– Hakka: Sin Ngien Kai Lok!
– Hokkien: Sin Nîn Khòai Lok!
– Mandarin: Xīn Nián Kuài Lè!
– Shanghainese: Cin Ni Khua Lo’!

Basque: Urte berri on

Cherokee: alihelisdi ije’i udetiyvsadish

Esperanto: Bonan novan jaron!

Sjal: Uura lon end!