Carbon nanotubes (CNT) have a very large application potential in the rapid developing field of molecular electronics. Infinite single-wall metallic CNTs have theoretically a conductance of 4e/h because of the two electronic bands crossing the Fermi level. For finite size CNTs experiments have shown that other values are also possible, indicating a very strong influence of the contacts. We study electron transport in single- and double-wall CNTs contacted to metallic electrodes within the Landauer formalism combined with Green function techniques. We show that the symmetry of the contact region may lead to blocking of a transport channel. In the case of double-wall CNTs with both inner and outer shells being metallic, non-diagonal self energy contributions from the electrodes may induce channel mixing, precluding a simple addition of the individual shell conductances.