There are many situations in which we would wish someone "Good luck!", for instance when someone is embarking in something difficult or dangerous. How can we express a similar thing in Italian?
The "neutral" way is the literal translation:
The more colloquial way (not rude or offensive, can generally be used with anyone, though it might depend on the situation) is an idiomatic expression:
In bocca al lupo!
to which the person who is wished luck usually replies:
Crepi (il lupo)!
"Buona fortuna" is the literal translation of "Good luck".
If you're in an informal context (eg talking to friends), you may want to use "In bocca al lupo" (literally: [go] into the wolf's mouth) instead.
I'll depart from the obvious answers, and suggest you to say: "Auguri!".
This is the most neutral greeting in most cases: no particular register, doesn't assume a good or bad occasion, doesn't invoke the sorte etc. Can sometimes be sarcastic; but if you are sincere it won't, just like "Good luck".
I'm pointing this alternative out because it happens to me almost daily that I think "Auguri!" for someone who only speaks English, but I'm prevented from saying it because in English any translation may be ambiguous.