We study plasmonic waveguides with dielectric cores and hyperbolic multilayer claddings. The proposed design provides better performance in terms of propagation length and mode confinement in comparison to conventional designs, such as metal-insulator-metal and insulator-metal-insulator plasmonic waveguides. We show that the proposed structures support long-range surface plasmon modes, which exist when the permittivity of the core matches the transverse effective permittivity component of the metamaterial cladding. In this regime, the surface plasmon polaritons of each cladding layer are strongly coupled, and the propagation length can be on the order of a millimeter.