We studied the electrical conductivity of DNA molecules with conducting atomic force microscopy as a function of the chemical nature of the substrate surfaces, the nature of the electrical contact, and the number of DNA molecules (from a few molecules, to ropes and large fibers containing up to ~ 106 molecules). Independent of the chemical nature of the surface (hydrophobic or hydrophilic, electrically neutral or charged), we find that DNA is highly resistive. From a large number of current-voltage curves measured at several distance along the DNA, we estimate a conductivity of about 10-6-10-5 S·cm-1 per DNA molecule. For single DNA molecules, this highly resistive behavior is correlated with its flattened conformation on the surface (reduced thickness, ~0.5-1.5 nm, compared to its nominal value, ~2.4 nm). We find that intercalating an organic semiconductor buffer film between the DNA and the metal electrode improves the reliability of the contact, while direct metal evaporation usually destroys the DNA and prevents any current measurements. After long exposure under vacuum or dry nitrogen, the conductivity strongly decreases, leading to the conclusion that water molecules and ions in the hydration shell of the DNA play a major role.