The captains dinner is usually the first "formal" night, so wear your best. Depending on your cruise, there could also be a semi formal night, and you also wear a nice dress, just not as formal as the 2 formals on a 7 day cruise. The guys wear black suits or tux's. The rest of the nights are casual, wear nice pants suits, sun dresses, the guys can wear docker type pants and polo shirts then.
Here is a link to help with what you'll need to pack: