* ταχύς (tachýs): This is a good general word for "fast" referring to speed or quickness.
* οξύς (oxýs): This word implies sharpness or acuteness, and can be used for things that happen quickly and intensely.
* swift (σβίφτ): This is a loanword from English, often used in modern Greek, particularly in contexts where "fast" refers to speed (e.g., a fast car).
The best choice will depend on what is moving quickly. For example, a "fast car" might be ταχύ αυτοκίνητο (tachý aftokínito), while a "fast runner" could be ταχύς δρομέας (tachýs droméas).