What are the arguments for and against electing judges rather than executive appointment or legislative selection?

The first is the appointment method, in which the executive of the state nominates an individual to become a judge, and (usually) the state senate must confirm the nominee before he or she takes office. The second method is known as “retention elections,” in which the executive will appoint a judge to the bench, and then after a certain term, voters are asked whether or not they want to retain the judge. Finally, there are “competitive elections,” in which judges run for their seat in more or less the same way that other elected officials run for office: they are nominated by a party (usually through a primary election), and then they run against a nominee from the other party in the general election. 

in griswold v. connecticut (1965), the supreme court ruled that a state's ban on the use of contraceptives violated the right to marital privacy.