I'm going on a short (four night) cruise on October 1, and it states that there will be one formal night. You may be able to eat at one of the less formal restaurants on the ship if you don't want to pack suits and cocktail dresses.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)