A pair of capuchin monkeys (Cebus apella) show very compelling signs of cooperation and a sense of fairness, by working together to solve a problem using tools, and then sharing the reward.
They also seem to understand fairness: when unequal rewards are given to one monkey and not another, the monkey receiving the lesser treat would rather go hungry than accept anything less than an equal reward.
The token exchange from the latter half of the video is interesting in and of itself; I'm sure it took a lot of training. There is another example of its usage by the same experimenter here: http://youtube.com/watch?v=aAFQ5kUHPkY
From the BBC documentary "Capuchins: The Monkey Puzzle", narrated by the ever brilliant Sir David Attenborough.