I believe the republic existed before the empire reference Star Wars: Episode one, where Chancellor Palpataine (I belive that's his name) is seen talking to a rather large council in floating boxes

. I do not believe that we were told if the members of the council were elected or not. The Jedi Council seems to be representative body however I do not believe that we are told if one is elected to that body or not

. I believe the sith are the only ones with a monarchy.