Context. GJ 1214b, the 6.55 Earth-mass transiting planet recently discovered by the MEarth team, has a mean density of ∼35% of that of the Earth. It is thought that this planet is either a mini-Neptune, consisting of a rocky core with a thick, hydrogen-rich atmosphere, or a planet with a composition dominated by water. Aims. In the case of a hydrogen-rich atmosphere, molecular absorption and scattering processes may result in detectable radius variations as a function of wavelength. The aim of this paper is to measure these variations. Methods. We have obtained observations of the transit of GJ 1214b in the r-and I-band with the Isaac Newton Telescope (INT), in the g-, r-, i-and z-bands with the 2.2 m MPI/ESO telescope, in the K s -band with the Nordic Optical Telescope (NOT), and in the K c -band with the William Herschel Telescope (WHT). By comparing the transit depth between the the different bands, which is a measure for the planet-to-star size ratio, the atmosphere is investigated. Results. We do not detect clearly significant variations in the planet-to-star size ratio as function of wavelength. Although the ratio at the shortest measured wavelength, in g-band, is 2σ larger than in the other bands. The uncertainties in the K s and K c bands are large, due to systematic features in the light curves. Conclusions. The tentative increase in the planet-to-star size ratio at the shortest wavelength could be a sign of an increase in the effective planet-size due to Rayleigh scattering, which would require GJ 1214b to have a hydrogen-rich atmosphere. If true, then the atmosphere has to have both clouds, to suppress planet-size variations at red optical wavelengths, as well as a sub-solar metallicity, to suppress strong molecular features in the near-and mid-infrared. However, star spots, which are known to be present on the hoststar's surface, can (partly) cancel out the expected variations in planet-to-star size ratio, because the lower surface temperature of the spots causes the effective size of the star to vary with wavelength. A hypothetical spot-fraction of ∼10%, corresponding to an average stellar dimming of ∼5% in the i-band, would be able to raise the near-and mid-infrared points sufficiently with respect to the optical measurements to be inconsistent with a water-dominated atmosphere. Modulation of the spot fraction due to the stellar rotation would in such case cause the observed flux variations of GJ 1214.