We have observed 23 class 0 sources in the HCO⁺ J = 4–3 and 3–2 lines. The mean bolometric temperature of the 16 sources with well-determined values is 44 K, and the mean luminosity is 5.7 L, excluding two sources of considerably higher luminosity. Nine sources, including three sources previously suggested to be collapsing, have the correct (blue) spectral line asymmetry for infall in both lines. Three sources have the opposite (red) asymmetry in both lines, and one source, L1157, has a red asymmetry in HCO⁺ J = 4–3 and a blue asymmetry in J = 3–2. The rest have no significant or consistent asymmetry. The H¹³CO⁺ J = 4–3 and 3–2 lines were also observed to find the velocity of the ambient gas, and sources with an interesting line asymmetry were mapped. A Monte Carlo code was used to produce an evolutionary sequence of collapsing cloud models of the HCO⁺ J = 4–3 and 3–2 lines and to compare various diagnostics of the resulting line profiles. The same code was used to compare infall models to the observations in one source, L1527. The results were consistent with previous collapse models. Based on integrated intensity maps of the line peaks and wings, as well as the velocity of the H13CO⁺ line, we select six of the nine sources with a blue line asymmetry as good candidates for protostellar collapse. Further evidence is needed to establish that infall is taking place. The HCO⁺ spectra are not conclusive because bipolar outflows produce strong emission, which can confuse the issue in any individual source. However, the predominance of blue asymmetries over red asymmetries is not naturally explained in outfow models, whereas it is expected in collapse models.