Formal:
* פאַרמאַכט זיך! (far-makt zikh!) - Literally "Close yourself!", but used as a polite way to say goodbye, similar to "Take care!"
* אַדיו (adieu) - This is the more formal and direct translation of "goodbye".
Informal:
* אַ גוטן טאָג! (a gutn tog!) - "Have a good day!"
* שָׁלוֹם (shalom) - "Peace" or "goodbye", used as a more general greeting and farewell.
* זיי געזונט (zay gezunt) - "Be healthy" or "Take care".
* ביז דעם קומענדיקן מאָל (biz dem kumendikn mol) - "Until next time."
Slang:
* טשיוס (tchius) - A shortened form of "chau" (short for "chau-chau", a German word for "goodbye"), similar to "Ciao".
* טשיקס (tchiks) - A more informal way to say "goodbye", similar to "later".
The best choice will depend on the situation and your relationship with the person you're saying goodbye to.