"Dark beams" are nonuniform optical beams that contain either a one-dimensional (1D) dark stripe or a two-dimensional (2D) dark hole resulting from a phase singularity or an amplitude depression in their optical field. Thus far, self-trapped dark beams (dark solitons) have been observed using coherent light only. Here, self-trapped dark incoherent light beams (self-trapped dark incoherent wavepackets) were observed. Both dark stripes and dark holes nested in a broad partially spatially incoherent wavefront were self-trapped to form dark solitons in a host photorefractive medium. These self-trapped 1D and 2D dark beams induced refractive-index changes akin to planar and circular dielectric waveguides. The experiments introduce the possibility of controlling high-power coherent laser beams with low-power incoherent light sources such as light emitting diodes.