Variant forms change by gender and number- Benvenuto to a man, Benvenuti to two or more men or a mixed group, Benvenuta to a woman, Benvenute to two or more women.
The list is not exhaustive. There is no equivalent to the English Good riddance (French Bon debarras).
Buon Natale Merry Christmas
Buon Anno Happy New Year, Felice Capodanno (sometimes) if it follows Buon Natale, especially when written.
Buona Pasqua Happy Easter
Buon Pesach Happy Passover
Buon Compleanno Happy Birthday
Buon Onomastico Happy Name Day (practically fallen into disuse)
Buone Feste Happy Holidays
Ben tornato/i/a/e Welcome back
Ben arrivato/i/a/e Welcome (of someone who has made a trip, even short)
Ben trovato/i/a/e To someone one meets again, usually unexpectedly
Ben ritrovato/i/a/e To someone one meets after an absence
Buon lavoro To those who are working or starting a task
Buon proseguimento To those who are continuing something interrupted
Buon riposo Have a good rest
Buona fortuna Good luck
Buon appetito Like French Bon appetit, before a meal. Enjoy!
Buon pranzo Have a good lunch
Buon viaggio Like French Bon voyage, before a trip
Buon giorno Good morning/day (roughly used during daylight hours)
Buon pomeriggio Used (not often) in mid-afternoon
Buona sera Good evening, used roughly after daylight has ended
Buona notte Good night
Buone vacanze Have a good vacation
Buona permanenza Have a good stay
Buon fine settimana/week-end Have a good weekend
Buona domenica Have a good Sunday
Buone cose/Tante buone cose (somewhat old-fashioned) Generic well-wishing; literally, Good things