Porous yet densely packed carbon electrodes with high ion-accessible surface area and low ion transport resistance are crucial to the realization of high-density electrochemical capacitive energy storage but have proved to be very challenging to produce. Taking advantage of chemically converted graphene's intrinsic microcorrugated two-dimensional configuration and self-assembly behavior, we show that such materials can be readily formed by capillary compression of adaptive graphene gel films in the presence of a nonvolatile liquid electrolyte. This simple soft approach enables subnanometer scale integration of graphene sheets with electrolytes to form highly compact carbon electrodes with a continuous ion transport network. Electrochemical capacitors based on the resulting films can obtain volumetric energy densities approaching 60 watt-hours per liter.