We present a survey of the formaldehyde emission in a sample of eight Class 0 protostars obtained with the IRAM and JCMT millimeter telescopes. The range of energies of the observed transitions allows us to probe the physical and chemical conditions across the protostellar envelopes. The data have been analyzed with three different methods with increasing level of sophistication. We first analyze the observed emission in the LTE approximation, and derive rotational temperatures between 11 and 40 K, and column densities between 1 and 20 × 10¹³ cm^-2. Second, we use a LVG code and derive higher kinetic temperatures, between 30 and 90 K, consistent with subthermally populated levels and densities from 1 to 6 × 10⁵ cm^-3. The column densities from the LVG modeling are within a factor of 10 with respect to those derived in the LTE approximation. Finally, we analyze the observations based upon detailed models for the envelopes surrounding the protostars, using temperature and density profiles previously derived from continuum observations. We approximate the formaldehyde abundance across the envelope with a jump function, the jump occurring when the dust temperature reaches 100 K, the evaporation temperature of the grain mantles. The observed formaldehyde emission is well reproduced only if there is a jump of more than two orders of magnitude, in four sources. In the remaining four sources the data are consistent with a formaldehyde abundance jump, but the evidence is more marginal (≤2 σ). The inferred inner H₂CO abundance varies between 1 × 10^-8 and 6 × 10 ^-6. The absolute values of the jump in the H₂CO abundance are uncertain by about one order of magnitude, because of the uncertainties in the density, ortho to para ratio, temperature and velocity profiles of the inner region, as well as the evaporation temperature of the ices. We discuss the implications of these jumps for our understanding of the origin and evolution of ices in low mass star forming regions. Finally, we give predictions for the submillimeter H₂CO lines, which are particularly sensitive to the abundance jumps.