Evolutionary game theory describes the temporal development of different interacting strategies. Within the standard formulation, the dynamics is expressed by replicator equations. While this approach includes the basic driving force of evolution - selection by fitness differences - it is a deterministic one and does not take fluctuations into account. These fluctuations however, can be of enourmous importance and can even render evolution effectively neutral, fitness advantages can be ignored. Here, we quantify the role of fluctuations within evolutionary game theory by considering extinction events. We investigate the effects of selection versus fluctuations in general social dilemmas (i.e. general symmetric two-player games). By studying the mean extinction time, a variable sensitive to fluctuations, we are able to identify and quantify an emerging 'edge of neutral evolution' which delineates regimes of neutral and selection dominated evolution.