Combining the precise parallaxes and optical photometry delivered by Gaia's second data release with the photometric catalogues of Pan-STARRS1, 2MASS, and AllWISE, we derived Bayesian stellar parameters, distances, and extinctions for 265 million of the 285 million objects brighter than G=18. Because of the wide wavelength range used, our results substantially improve the accuracy and precision of previous extinction and effective temperature estimates. After cleaning our results for both unreliable input and output data, we retain 137 million stars, for which we achieve a median precision of 5% in distance, 0.20mag in V-band extinction, and 245K in effective temperature for G<=14, degrading towards fainter magnitudes (12%, 0.20mag, and 245K at G=16; 16%, 0.23mag, and 260K at G=17, respectively). We find a very good agreement with the asteroseismic surface gravities and distances of 7000 stars in the Kepler, K2-C3, and K2-C6 fields, with stellar parameters from the APOGEE survey, and with distances to star clusters. Our results are available through the ADQL query interface of the Gaia mirror at the Leibniz-Institut fuer Astrophysik Potsdam (gaia.aip.de) and as binary tables at data.aip.de. As a first application, we provide distance- and extinction-corrected colour-magnitude diagrams, extinction maps as a function of distance, and extensive density maps. These demonstrate the potential of our value-added dataset for mapping the three-dimensional structure of our Galaxy. In particular, we see a clear manifestation of the Galactic bar in the stellar density distributions, an observation that can almost be considered direct imaging of the Galactic bar.