A key property of the Ising model is the critical point at which the system "spontaneously" magnetizes (in equilibrium). The focus of my talk is on the less understood non-equilibrium dynamics of ferromagnetic ordering following a quench below the critical point. It might be naively expected that the quenched system always reaches either the up or down equilibrium state. Surprisingly, the system sometimes becomes dynamically trapped in a non-equilibrium configuration of striped magnetic domains. By employing a surprising connection to critical percolation, we find that in two dimensions this trapping occurs with the universal probability of 0.3388 ... , independent of many system details. In more than two dimensions the correspondence to critical percolation is lost, and the potentially richer dynamics is investigated via simulation.