We present an investigation of the transmission spectrum of the 6.5 M(circle plus) planet GJ 1214b based on new ground-based observations of transits of the planet in the optical and near-infrared, and on previously published data. Observations with the VLT + FORS and Magellan + MMIRS using the technique of multi-object spectroscopy with wide slits yielded new measurements of the planet's transmission spectrum from 0.61 to 0.85 mu m, and in the J, H, and K atmospheric windows. We also present a new measurement based on narrow-band photometry centered at 2.09 mu m with the VLT + HAWKI. We combined these data with results from a reanalysis of previously published FORS data from 0.78 to 1.00 mu m using an improved data reduction algorithm, and previously reported values based on Spitzer data at 3.6 and 4.5 mu m. All of the data are consistent with a featureless transmission spectrum for the planet. Our K-band data are inconsistent with the detection of spectral features at these wavelengths reported by Croll and collaborators at the level of 4.1 sigma. The planet's atmosphere must either have at least 70% H(2)O by mass or optically thick high-altitude clouds or haze to be consistent with the data.