Measurements of the plasma potential, electron density, effective electron temperature, and electron energy distribution function (EEDF) have been performed with Langmuir probes in planar, electrostatically shielded, low-pressure inductively coupled plasmas. The plasma source is a modification of the Gaseous Electronics Conference RF Reference Cell [P. J. Hargis {ital et al.}, Rev. Sci. Instrum. {bold 65}, 140 (1994)] with the upper electrode replaced by a five-turn planar coil and a quartz vacuum interface. Four different rare gases (Ar, Kr, Xe, and Ne), a He:Ar (96:4) mixture, and O{sub 2} and N{sub 2} were investigated. We found that with increasing ionization potential of the rare gas the electron density decreases, while the effective electron temperature and the plasma potential increase. Non-Maxwellian EEDFs were observed for all energies for O{sub 2} and N{sub 2} discharges as well as for the rare gases above the energy range for elastic collisions. Spatially resolved measurements confirm that the EEDF is determined by spatially averaged quantities instead of the local electric field. {copyright} {ital 1997} {ital The American Physical Society}