Following our recent idea of using plasmonic and nonplasmonic nanoparticles as nanoinductors and nanocapacitors in the infrared and optical domains [N. Engheta et al., Phys. Rev. Letts. 95, 095504 (2005)], in this work we analyze in detail some complex circuit configurations involving series and parallel combinations of these lumped nanocircuit elements at optical frequencies. Using numerical simulations, it is demonstrated that, after a proper design, the behavior of these nanoelements may closely mimic that of their lower-frequency [i.e., radio frequency (rf) and microwave] counterparts, even in relatively complex configurations. In addition, we analyze here in detail the concepts of nanoinsulators and nanoconnectors in the optical domain, demonstrating how these components may be crucial in minimizing the coupling between adjacent optical nanocircuit elements and in properly connecting different branches of the nanocircuit. The unit nanomodules for lumped nanoelements are introduced as building blocks for more complex nanocircuits at optical frequencies. Numerical simulations of some complex circuit scenarios considering the frequency response of these nanocircuits are presented and discussed in detail, showing how practical applications of such optical nanocircuit concepts may indeed be feasible within the current limits of nanotechnology.