Following our recent theoretical development of the concept of nano-inductors, nano-capacitors and nano-resistors at optical frequencies and the possibility of synthesizing more complex nanoscale circuits, here we theoretically investigate in detail the problem of optical nano-transmission lines (NTL) that can be envisioned by properly joining together arrays of these basic nano-scale circuit elements. We show how, in the limit in which these basic circuit elements are closely packed together, the NTLs can be regarded as stacks of plasmonic and non-plasmonic planar slabs, which may be designed to effectively exhibit the properties of planar metamaterials with forward (right-handed) or backward (left-handed) operation. With the proper design, negative refraction and left-handed propagation are shown to be possible in these planar plasmonic guided-wave structures, providing possibilities for sub-wavelength focusing and imaging in planar optics, and laterally-confined waveguiding at IR and visible frequencies. The effective material parameters for such NTLs are derived, and the connection and analogy between these optical NTLs and the double-negative and double-positive metamaterials are also explored. Physical insights and justification for the results are also presented.