This dissertation describes measurements of electron transport through single molecules in mechanically controllable break junctions. In the first two experiments, we study molecules in the Kondo regime at low temperature. We vary the electrode spacing to tune the spin- 1 Kondo effect 2 in a C60 molecule as well as its lowest-energy vibrational mode. In the second experiment, we achieve spin control in an organometallic cobalt complex by stretching the molecule, thereby breaking its symmetries. We also describe the fabrication of ferromagnetic-electrode devices for the study of spin-dependent transport through individual molecules and nanoparticles. Finally, we present the development of an instrument for the measurement of single-molecule conductances at room temperature by repeatedly forming and breaking contact between two gold surfaces in a molecular environment.