Generally speaking, cruise travel is very casual during the day and casual to formal in the evenings. This can vary depending on the itinerary. Caribbean, Hawaiian, Alaskan cruises are more informal while Transatlantic, Mediterranean and European cruises tend to be a little more formal. This can also vary from cruise line to cruise line and ship to ship.
Princess Cruise Line would probably lean toward formal whereas Carnival will tend to be more informal and casual. There is no real hard and fast rule, however, here's a try.
Men should always pack one dark suit which will usually suffice even on "formal night." You can take a tuxedo, but we recommend that you rent one on board the ship (most ships offer this service) unless you own one and just want the extra baggage. Tuxedos are generally not "required".
Ladies can take cocktail dresses or a full length formal.
There are usually 1 to 2 formal nights on a 7 night cruise, only 1 on 3 & 4 night cruises. The rest of the time is typically very casual. Even on "non-formal" nights, men should wear a collared shirt to dinner and slacks or skirts for the ladies.