We studied the propagation of plasmonic modes along planar multilayer metal-dielectric structures with finite number of bi-layer unit cells. The dispersion relations for various investigated waveguide structures with the multilayer core and symmetric or asymmetric cladding have been analyzed. In the case of symmetric metallic cladding we have found both TE and TM modes within the light cone, while TM modes only exist outside the light cone. Both symmetric and asymmetric dielectric claddings support modes outside the light cone and of TM-polarization only. Formation of photonic bands and gaps, the structure of their edge lines, and the behavior of modes that cross the edge lines has been investigated. In the subwavelength regime, we have found ordinary surface plasmon polariton dispersion in the forbidden gap that is created via coalescence of the two modes that cross the neighboring band-gap edges. One of those modes can exhibit negative group velocity.