Ballistic transport of electrons through conductors whose width is comparable with the electron Fermi wavelength is quantized in units of the quantum of conductance G₀. Using the tip of a cryogenic scanning tunnelling microscope we contact controllably and reproducibly single atoms and molecules adsorbed on metal surfaces. For noble and transition metal atoms we find a contact conductance of ~ G₀. Intriguingly, C₆₀ molecules exhibit conductances between ~ G₀/5 and ~ G₀/4 depending on their adsorption geometry on the surface. We further show that in contact with the tip, C₆₀ orientations can be switched reversibly. Latest results address spin-polarized transport through magnetic atoms.