There are many different ways of categorizing theories of government, but if I had to name a single dichotomy between two fundamental concepts of government it would be between Hobbes and Rousseau. Both of these theories are based on the idea of a "state of nature" that existed before governments, perhaps conceived as the state that human beings lived in 200,000 years ago.
Thomas Hobbes held that the state of nature was one of constant violence and competition; life was "nasty, brutish, and short" as he put it. On his view, government exists to restrain our base animal instincts and keep us from lapsing into our innate tendency toward violence. Hobbes favored a very strong government; indeed, in Leviathan he basically argues for a government with absolute, unquestioned power.
Jean-Jacques Rousseau, on the other hand, argued that human beings are naturally cooperative, compassionate, and kind. On his view, government was created by tyrants imposing their will on others, and far from protecting us, government was actually the source of most violence in the world. He suggested doing away with government entirely, or failing that, establishing a very weak government with very strong guarantees of freedom and accountability. He had a strong influence on the French Revolution and its ideals of liberty and democracy.
Which one is true? In my opinion, both extremes capture part of a more complex truth. In the study of human evolution we find both innate capacities for compassion and altruism, as well as for violence and hatred. Government does serve a vital function in protecting us from crime and invasion, but it must also be kept in check, limited in power and always held accountable to the people it is meant to serve. Democracy is the attempt to strike this delicate balance, and as Winston Churchill famously said: "Democracy is the worst form of government, except for all those others that have been tried."