We present Halpha rotation curves for a sample of 15 dwarf and LSB galaxies. From these, we derive limits on the slopes of the central mass distributions. Assuming the density distributions of dark matter halos follow a power-law at small radii, rho(r)~r^(-alpha), we find inner slopes in the range 0<alpha<1 for most galaxies. In general, halos with constant density cores (alpha=0) provide somewhat better fits, but the majority of our galaxies (~75%) are also consistent with alpha=1, provided that the R-band mass-to-light ratios are smaller than about 2. Halos with alpha=1.5, however, are ruled out in virtually every case. To investigate the robustness of these results we discuss and model several possible causes of systematic errors including non-circular motions, slit width, seeing, and slit alignment errors. Taking the associated uncertainties into account, we conclude that even for the 25% of the cases where alpha=1 seems inconsistent with the rotation curves, we cannot rule out cusp slopes this steep. Inclusion of literature samples similar to the one presented here leads to the same conclusion when possible systematic errors are taken into account. In the ongoing debate on whether the rotation curves of dwarf and LSB galaxies are consistent with predictions for a CDM universe, we argue that our sample and the literature samples discussed in this paper provide insufficient evidence to rule out halos with alpha=1. At the same time, we note that none of the galaxies in these samples require halos with steep cusps, as most are equally well or better explained by constant density cores. (abridged)
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