The breaking of waves is an important mechanism for a number of physical, chemical and biological processes in the ocean. Intuitively, waves break when they become too steep. Unfortunately, a general consensus on the ultimate shape of waves has not been achieved yet due to the complexity of the breaking mechanism which still remains the least understood of all processes affecting waves. To estimate the limiting shape of ocean waves, here we present a statistical analysis of a large sample of individual wave steepness. Data were collected from measurements of the surface elevation in laboratory facilities and the open sea under a variety of sea state conditions. Observations reveal that waves are able to reach steeper profiles than the Stokes' limit for stationary waves. Due to the large number of records this finding is statistically robust.