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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 atsmall radii, rho(r)~r^(-alpha), we find inner slopes in the range 0<alpha<1 formost galaxies. In general, halos with constant density cores (\alpha=0) providesomewhat better fits, but the majority of our galaxies (~75%) are alsoconsistent with alpha=1, provided that the R-band mass-to-light ratios aresmaller than about 2. Halos with alpha=1.5, however, are ruled out in virtuallyevery case. To investigate the robustness of these results we discuss and modelseveral possible causes of systematic errors including non-circular motions,slit width, seeing, and slit alignment errors. Taking the associateduncertainties into account, we conclude that even for the 25% of the caseswhere alpha=1 seems inconsistent with the rotation curves, we cannot rule outcusp slopes this steep. Inclusion of literature samples similar to the onepresented here leads to the same conclusion when possible systematic errors aretaken into account. In the ongoing debate on whether the rotation curves ofdwarf and LSB galaxies are consistent with predictions for a CDM universe, weargue that our sample and the literature samples discussed in this paperprovide 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 steepcusps, as most are equally well or better explained by constant density cores.(abridged)Comment: 19 pages, accepted for publication in Ap

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