In polar regions, highly adapted social behavior is crucial for the survival of several species. Prominent examples are the huddling behavior of Emperor Penguins, or the crèche (group) formation of King Penguin chicks. To understand how penguins solve the physical problem of movement in densely packed (jammed) groups, we observed Emperor Penguin huddles and King Penguin fledglings with time-lapse/video imaging, and used individual bird tracking and optical flow methods to analyze their movements. We found that Emperor Penguins overcome jamming by moving periodically in large, coordinated clusters. Every 30 - 60 seconds, all penguins make small steps, which travel as a wave through the entire huddle. Over time, these small movements lead to large-scale reorganization of the huddle. Groups of King Penguin fledglings moved in irregular intervals, often attributable to predator attacks, but the individual penguins in the group also moved collectively in a coordinated fashion to ensure the integrity of the group. Our data show that the dynamics of penguin huddling and group formation is governed by intermittency and approach to kinetic arrest in striking analogy with inert non-equilibrium systems. Basic aspects of this behavior can be reproduced with a simple model of interacting point particles. Individual animals are treated as self-driven agents with situation-dependent behavior, similar to simulations of collective swarm behavior in flocks and herds. Both the spontaneous huddle formation and the observed wave patterns emerge from simple rules that only encompass the interaction between directly neighboring individuals. As an important result, our model demonstrates that a collective movement can be triggered by a forward step of any individual within the dense huddle. It remains an open question, however, why individual penguins in a huddle trigger a movement, and by which mechanism the experimentally observed periodicity of huddle movement (~ 40 seconds) remains stable.