Any dynein complex that catalyzes movement along a cytoplasmic microtubule; cytoplasmic dynein complexes participates in many transport activities in eukaryotes, such as mRNA localization, intermediate filament transport, nuclear envelope breakdown, apoptosis, transport of centrosomal proteins, mitotic spindle assembly, virus transport, kinetochore functions, and movement of signaling and spindle checkpoint proteins. Subunits associated with the dynein heavy chain mediate association between dynein heavy chain and cargoes,and may include light chains and light intermediate chains.