We present high-resolution Hα rotation curves for a sample of 15 dwarf and low surface brightness galaxies. From these we derive limits on the slopes of the central mass distributions, using both a direct inversion of the rotation curves and detailed mass models. Assuming that the density distributions of dark matter halos follow a power law at small radii, ρ(r)~r-α, we find inner slopes in the range 0<~α<~1 for most galaxies. Thus, even with the relatively high spatial resolution of the Hα rotation curves presented here, the inner slopes are poorly constrained. In general halos with constant density cores (α=0) provide somewhat better fits, but the majority of our galaxies (~75%) are also consistent with α=1, as long as the R-band stellar mass-to-light ratios are smaller than about 2. Halos with α=1.5, however, are ruled out in virtually every case. In order to investigate the robustness of these results we discuss and model several possible causes of systematic errors, including noncircular motions, galaxy inclination, slit width, seeing, and slit alignment errors. Taking the associated uncertainties into account, we conclude that even for the ~25% of the cases where α=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 the possibility of systematic errors is taken into account. In the ongoing debate on whether the rotation curves of dwarf and low surface brightness galaxies are consistent with predictions for a cold dark matter universe, we argue that our sample and the literature samples discussed in this paper provide insufficient evidence to rule out halos with α=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 halos with constant density cores.