Despite a growing number of realizations in experiment the efficient numerical simulation of real time evolution of isolated quantum many-body systems far from equilibrium remains challenging. Especially, systems of intermediate spatial dimensions are still largely elusive to the established approaches. In this work we demonstrate that combining a time-dependent variational principle with deep neural networks as ansatz for the wave function yields a versatile and reliable method in the sense that it is not tailored to the specific problem and the error can be quantified and systematically reduced. A deep network architecture is particularly well suited to exploit the locality of physical dynamics for the representation of the time-evolved wave function. As a concrete example, we simulate the dynamics of the paradigmatic and experimentally relevant two-dimensional transverse field Ising model. The maximal times reached are comparable to or exceed the capabilities of state-of-the-art tensor network methods.