I think some terminology is the source of some confusion. I think there are two definitions of "free electrons" floating around in this thread. The OP used free electrons to refer to conductive electrons, electrons which act to conduct electricity. Enahs used "free electrons" to refer to lone pairs or electrons not involved in a chemical bond. These two descriptions of "free electrons" are not the same.
Conductive electrons, such as those found in metals or other conductive materials, are actually involved in chemical bonding. In a metal, all of the s-orbitals of the metal atoms form a large delocalized set of molecular orbitals which form a "band structure" (see
http://en.wikipedia.org/wiki/Band_theory). Electrons which are excited from the valence band to the conduction band (excitation in metals takes only thermal energy) can easily move about and conduct electricity.
A similar phenomenon occurs with conductive polymers and other conductive materials (e.g. graphite, carbon nanotubes). Here, the conductive electrons reside in a conjugated pi-bond system which is delocalized across the entire material, allowing the electrons to freely conduct electricity across the material.
In general, electrons residing in lone pairs or orbitals not involved in bonding will not be conductive at all since these orbitals are confined to one atom or one molecule only.