One example of a prisoner's dilemma resulting in cooperation is the infinitely/indefinitely repeating prisoner's dilemma (assuming the players don't discount the future too much).

(The non-repeated, one-shot prisoner's dilemma never results in cooperation. As the game theorist Ken Binmore explains in several of his books, among them Natural Justice, defection strongly dominates cooperation in the one-shot PD and it inexorably follows that a rational player never cooperates.)