We have investigated the (n,gamma) cross sections of p-process isotopes with the activation technique. The measurements were carried out at the Karlsruhe Van de Graaff accelerator using the 7Li(p,n)7Be source for simulating a Maxwellian neutron distribution of kT = 25 keV. Stellar cross section measurements are reported for the light p-process isotopes 102Pd, 120Te, 130,132Ba, and 156Dy. In a following paper the cross sections of 168Yb, 180W, 184Os, 190Pt, and 196Hg will be discussed. The data are extrapolated to p-process energies by including information from evaluated nuclear data libraries. The results are compared to standard Hauser-Feshbach models frequently used in astrophysics.