Throughout history, oligarchies have been tyrannical (relying on public obedience and/or oppression to exist) or relatively benign. Aristotle pioneered the use of the term as a synonym for rule by the rich, for which the exact term is plutocracy.
Oligarchy is not always rule by the wealthy, as oligarchs can simply be a privileged group, and do not have to be connected by bloodlines as in a monarchy.
Forms of government and other political structures associated with oligarchy can include aristocracy, Corporatocracy (Crony capitalism), meritocracy, military junta, plutocracy, technocracy, and theocracy.
Ancient Sparta, for instance, was run by an oligarchy.