There are many ways to say "nice to meet you" in any language. In fact, the whole concept of what manners to use and not to use should take up its own node. There are lots of little details, like what gestures not to make, and the difference in meaning between "nice to meet you" and "nice meeting you." (one is usually said when you are leaving) I encourage you to learn one of these and say it to any of your native speaking friends, it's great when their face lights up when they hear it.

Albanian: Më bëhet qejfi që u njohëm.
Arabic: Foursa sa'eeda (Literally "Happy Occasion")
Bangla: Apna ki dekhe kushi holam
Bulgarian: Priyatno mi e da se zapoznaem
Catalan: Encantat de coneixe't
Danish: Hyggeligt at moede dig
Dutch: "Aangenaam" or "Prettig kennis te maken" (the last one is rather formal and weird)
Finnish: Kiva tavata
French: Enchanté (m). / Enchantée (f). OR Je suis heureux de faire votre connaissance
German: Schöen dich zu sehen
Greek: Xarika gia tin gnorimia
Hebrew: Naim me'od (very pleasant)
Italian: Piacere di conoscerti (informal) / conoscerla (formal) / conoscervi (plural)
Japanese: Douzo yoroshiku
Persian(Farsi): Khosh'halam az di'dane sho'ma OR Az molaaghaate shoma khoshbakhtam (formal)
Polish: Mil/o mi cie, Pana Pania, poznac'
Russian: Rad znakomstvu OR Priyatno poznakomitsa
Sindarin: mae govannen (well met)
Spanish: Encantado (masc.) OR Encantada (fem.) de conocerle (formal) OR conocerte (informal)
Swedish: Trevligt att traeffas (not often used in Swedish)
Tamil: Ungallai sandhitadil miga magzhirchi
Turkish: Tani,stž-gžmžza memnun oldum.
Urdu: Aap se mil kar khushi hui (formal)

Note: Many of these are off the top of my head, and others from the web. I can't be positive how correct some of them are. If you know any more, please /msg me and I'll add it.

For some non-phonetic languages, see

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