Context. The sample of hot Jupiters that have been studied in great detail is still growing. In particular, when the planet transits its host star, it is possible to measure the planetary radius and the planet mass (with radial velocity data). For the study of planetary atmospheres, it is essential to obtain transit and occultation measurements at multiple wavelengths. Aims: We aim to characterize the transiting hot Jupiter WASP-19b by deriving accurate and precise planetary parameters from a dedicated observing campaign of transits and occultations. Methods: We have obtained a total of 14 transit lightcurves in the r'-Gunn, I-Cousins, z'-Gunn, and I + z' filters and 10 occultation lightcurves in z'-Gunn using EulerCam on the Euler-Swiss telescope and TRAPPIST. We also obtained one lightcurve through the narrow-band NB1190 filter of HAWK-I on the VLT measuring an occultation at 1.19 μm. We performed a global MCMC analysis of all new data, together with some archive data in order to refine the planetary parameters and to measure the occultation depths in z'-band and at 1.19 μm. Results: We measure a planetary radius of Rp = 1.376 ± 0.046 RJ, a planetary mass of Mp = 1.165 ± 0.068 MJ, and find a very low eccentricity of e = 0.0077-0.0032+0.0068, compatible with a circular orbit. We have detected the z'-band occultation at 3σ significance and measure it to be δFocc,z' = 352 ± 116 ppm, more than a factor of 2 smaller than previously published. The occultation at 1.19 μm is only marginally constrained at δFocc,NB1190 = 1711-726+745 ppm. Conclusions: We show that the detection of occultations in the visible range is within reach, even for 1 m class telescopes if a considerable number of individual events are observed. Our results suggest an oxygen-dominated atmosphere of WASP-19b, making the planet an interesting test case for oxygen-rich planets without temperature inversion. Based on photometric observations made with HAWK-I on the ESO VLT/UT4 (Prog. ID 084.C-0532), EulerCam on the Euler-Swiss telescope and the Belgian TRAPPIST telescope, as well as archive data from the Faulkes South Telescope, CORALIE on the Euler-Swiss telescope, HARPS on the ESO 3.6 m telescope (Prog. ID 084-C-0185), and HAWK-I (Prog. ID 083.C-0377(A)).The photometric time series data in this work are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/552/A2