The past decades have seen amazing progress in the fabrication of ever-smaller electronic devices. However, silicon-based electronics will not continue to shrink in size and cost indefinitely, and the current generation of devices is fast approaching various physical and economic barriers to their fabrication and operation. Hence there is critical interest in radical alternatives. One approach to nanofabrication is the use of self-assembly, where atoms spontaneously form nanometer scale structures under certain growth conditions. The question arises as to whether or not it is possible to use self-assembly to create useful structures such as an atomic or nanometer scale wire. Two examples will be presented. Some metals form one dimensional rows on the Si(001) surface that can be described as "single atom wide wires". These are the smallest "wires" imaginable, being one atom in cross section. However, they turn out to be too small to be truly useful. Our more recent work has focussed on growth of rare-earth (RE) silicide nanowires on silicon. Atomic resolution scanning tunneling microscopy shows that these wires are typically between 3 and 10 nm wide, 0.5 to 1 nm high, and 100 - 1000 nm long. Of all of the metal on silicon systems that we know of, the RE silicides are the most promising candidates for making nanowires with desirable properties such as nanometer lateral dimension, crystalline structure with low defect density, metallic conduction, and micron scale length. In the broader context of nanotechnology, scientists from Hewlett Packard have proposed using this type of wire as an interconnect in a self-assembled array of molecular switches.