The standard cold dark matter (CDM) model has recently been challenged by the claim that dwarf galaxies have dark matter halos with constant density cores, whereas CDM predicts halos with steeply cusped density distributions. Consequently, numerous alternative dark matter candidates have recently been proposed. In this paper, we scrutinize the observational evidence for the incongruity between dwarf galaxies and the CDM model. To this end, we analyze the rotation curves of 20 late-type dwarf galaxies studied by Swaters (1999). Taking the effects of beam-smearing and adiabatic contraction into account, we fit mass models to these rotation curves with dark matter halos with different cusp slopes, ranging from constant density cores to r cusps. Uncertainties in the stellar mass-to-light ratio and the limited spatial sampling of the halo’s density distribution hamper a unique mass decomposition. Consequently, the rotation curves in our sample cannot be used to discriminate between dark halos with constant density cores and r cusps. We show that the dwarf galaxies analyzed here are consistent with cold dark matter halos in a ΛCDM cosmology, and that there is thus no need to abandon the idea that dark matter is cold and collisionless. However, the data is also consistent with any alternative dark matter model that produces dark matter halos with central cusps less steep than r. In fact, we argue that based on existing rotation curves alone at best weak limits can be obtained on cosmological parameters and/or the nature of the dark matter. Subject headings: dark matter — galaxies: halos — galaxies: kinematics and dynamics — galaxies: fundamental parameters — galaxies: structure.