We consider a class of Nash games, termed as aggregative games, being played over a distributed networked system. In an aggregative game, an agent's objective function is coupled through a function of the aggregate of all agents' decisions. Every agent maintains an estimate of the aggregate and agents exchange this information locally with their neighbors over a connected network. We study distributed synchronous and asynchronous algorithms for information exchange and computation of equilibrium decisions of agents over the network. Under some standard conditions on the players' communication graph and the player' step-size choices, for both synchronous and asynchronous update rules, we establish the almost-sure convergence of the algorithms to an equilibrium point. In addition, we also present numerical results to assess the performance of the algorithms.