A key issue in research on ferrofluids (dispersions of magnetic colloids) is the effect of dipolar interactions on their structure and phase behaviour, which is not only important for practical applications but gives fundamental insight in dipolar fluids in general. In 1970, de Gennes and Pincus predicted a Van der Waals-like phase diagram and the presence of linear chains of particles in ferrofluids in zero magnetic field. Despite many experimental studies, no direct evidence of the existence of linear chains of dipoles has been reported in the absence of magnetic field, although simulations clearly show the presence of chain-like structures. Here, we show in situ linear dipolar structures in ferrofluids in zero field, visualized on the particle level by electron cryo-microscopy on thin, vitrified films of organic dispersions of monodisperse metallic iron particles. On systematically increasing the particle size, we find an abrupt transition from separate particles to randomly oriented linear aggregates and branched chains or networks. When vitrified in a permanent magnetic field, these chains align and form thick elongated structures, indicating lateral attraction between parallel dipole chains. These findings show that the experimental model used is well suited to study the structural properties of dipolar particle systems.