The charge transport and conductance measurement of a single atom or moiety, is an intriguing, experimentally challenging, and long sought goal. We have developed a number of techniques for the electrical measurement of single and/or few molecule systems. First, we have measured the electrical transport properties of a single molecule self-assembled onto the electrodes of a mechanically controllable break junction, allowing for direct observation of charge transport through the molecules. Current voltage I(V) measurements at room temperature demonstrate a highly reproducible apparent gap at about 0.7 V and a corresponding resistance of 22 MOhms. Second, we have developed a nanostructure device technique called a "nanopore" approach to measure the electronic transport of a class of stable self-assembled conjugated oligomers. This has allowed us to determine the barrier heights and transport mechanisms in these conjugated oligomer systems. We have also measured for the first time the molecular equivalent of a resonant tunneling device, and experimental results on a new molecular switching mechanism.