It is well known that the spin angular momentum of light, and therefore that of photons, is directly related to their circular polarization. Naturally, for totally unpolarized light, polarization is undefined and the spin vanishes. However, for non-paraxial light, the recently discovered transverse spin component, orthogonal to the main propagation direction, is largely independent of the polarization state of the wave. Here, we demonstrate, both theoretically and experimentally, that this transverse spin survives even in non-paraxial fields (for example, focused or evanescent) generated from totally unpolarized paraxial light. This counterintuitive phenomenon is closely related to the fundamental difference between the meanings of ‘full depolarization’ for two-dimensional (2D) paraxial and 3D non-paraxial fields. Our results open an avenue for studies of spin-related phenomena and optical manipulation using unpolarized light.A theoretical and experimental study of the transverse spin appearing in non-paraxial light when the source is totally unpolarized is reported, in sharp contrast to the usual longitudinal spin, which is directly related to the 2D polarization and vanishes in unpolarized fields.