Context: The interpretation of water line emission from infrared and submillimetre observations requires a detailed knowledge of collisional rate coefficients over a wide range of levels and temperatures. Aims: We attempt to determine rotational and rovibrational rate coefficients for H2O colliding with both H2 and electrons in warm, molecular gas. Methods: Pure rotational rates are derived by extrapolating published data using a new method partly based on the information (phase space) theory of Levine and co-workers. Ro-vibrational rates are obtained using vibrational relaxation data available in the literature and by assuming a complete decoupling of rotation and vibration. Results: Rate coefficients were obtained for the lowest 824 ro-vibrational levels of H2O in the temperature range 200-5000 K. Our data is expected to be accurate to within a factor of ~5 for the highest rates (?10-11 cm3 s-1). Smaller rates, including the ro-vibrational ones, should be generally accurate to within an order of magnitude. As a first application of this data, we show that vibrationally excited water emission observed in evolved stars is expected to be at least partly excited by means of collisions. Tables A.1-A.4 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/492/257