Most objects in the Build menu have a happiness rating, particularly under the Happiness, Decorations and Wonders tabs. Farms appear to be the best at providing happiness for their size and cost.
Your empire's Happiness is the sum total off all the happiness of all objects currently on your island (also in the waters nearby).
Objects deleted remove their happiness from your Empire Happiness total. Objects placed in storage also remove their happiness from your empire. Only objects currently on your island count towards your total happiness. (Taking objects back out of storage may sometimes need you to save the game and refresh to get the Happiness stat to increase back. )
Having more Happiness than Capacity will make the face in the upper right smile. If the capacity of the empire is more than the happiness, the face will frown. (If Capacity == Happiness, you also get the frown)
As of June 2010 there are several reported problems from users trying to have 50,000 population or more, so this is not recommended.