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(Abridged) Water is a key tracer of dynamics and chemistry in low-massprotostars, but spectrally resolved observations have so far been limited insensitivity and angular resolution. In this first systematic survey ofspectrally resolved water emission in low-mass protostellar objects, H2O wasobserved in the ground-state transition at 557 GHz with HIFI on Herschel in 29embedded Class 0 and I protostars. Complementary far-IR and sub-mm continuumdata (including PACS data from our program) are used to constrain the spectralenergy distribution of each source. H2O intensities are compared to inferredenvelope and outflow properties and CO 3-2 emission. H2O emission is detectedin all objects except one. The line profiles are complex and consist of severalkinematic components. The profiles are typically dominated by a broad Gaussianemission feature, indicating that the bulk of the water emission arises inoutflows, not the quiescent envelope. Several sources show multiple shockcomponents in either emission or absorption, thus constraining the internalgeometry of the system. Furthermore, the components include inverse P-Cygniprofiles in 7 sources (6 Class 0, 1 Class I) indicative of infalling envelopes,and regular P-Cygni profiles in 4 sources (3 Class I, 1 Class 0) indicative ofexpanding envelopes. "Bullets" moving at >50 km/s are seen in 4 Class 0sources; 3 of these are new detections. In the outflow, the H2O/CO abundanceratio as a function of velocity is nearly the same for all sources, increasingfrom 10^-3 at <5 km/s to >10^-1 at >10 km/s. The H2O abundance in the outerenvelope is low, ~10^-10. The different H2O profile components show a clearevolutionary trend: in the Class 0 sources, emission is dominated by outflowcomponents originating inside an infalling envelope. When the infall diminishesduring the Class I phase, the outflow weakens and H2O emission disappears.

Water in star-forming regions with Herschel (WISH): II. Evolution of 557 GHz 110-101 emission in low-mass protostars