I wish I had read this question sooner, for it is excellent!
In the field of psychology and education, Jean Jacques Rousseau has an amazing similarity with Sigmund Freud in their views of the individual and society: They both basically state a believe in the "basic Id"- However, while Freud believed that we are all born inherently bad and society has the chance to turn us into fitting citizens, JJ Rousseau thought the opposite:That we have an inherently good nature and society corrupts us.
In not so many words: Society makes us bad because of the plentitude of exposure we get to potentially damaging influences.
(its funny that Rousseau would take a stand in behaviorism, especially coming from a person who put his kids in an orphanage, was a bad teacher, and had immense flaws, yet- his philosophy transformed our field and continues doing so)
The first answer gives a really good view of Rousseau's vision of the relationship between individual and society. I will address the relationships between societies.
This is very much related to the question you asked last night. Rousseau believes that, sadly, countries (or societies) as a whole do not have the amour propre. Instead, they feel the amour de soi and see other societies as objects rather than as ends in themselves (to borrow the first answerer's borrowing from Kant). Because of this, different nations do not try to interact with each other based on an enlightened self interest. Instead, they try to exploit one another as much as possible.
For Rousseau, all issues of social and personal interaction are rooted in how an individual views themselves. Rousseau identifies two types of self love, or perception of oneself. The first kind is what Rousseau considers healthy or proper. This form of self love, amour propre, is when individuals have a view of themselves that is centered on viewing oneself not in antagonism with others, but rather as a complete sense of self that will allow to perceive others in a manner that is not competitive. The opposite of this would be amour de soi, which is a form of self love that is rooted in how others perceive an individual. In this form of self love, one is trapped by the gazes of another, and views consciousness through the eyes of others and is poised in competition with one another because there is little in way of being centered and settled. The individualism and antagonism against social notions of the good, when individuals view others as means to ends as opposed to an end in of itself (to borrow a bromide from Kant) is a reflection of amour de soi. For Rousseau, society should be organized in a manner that enhances amour propre, and minimizes amour de soi. If societies fail to do this, strife, antagonism, and discontent will reign supreme and any hope of cooperative and participatory frameworks will be negated.