  We use the rotation curves of a sample of dark matter dominated dwarf and
low-surface brightness (LSB) late-type galaxies to study their radial mass
distributions. We find that the shape of the rotation curves is remarkably
similar for all (both dwarf and LSB) galaxies in the sample, suggesting a
self-similar density distribution of their dark matter (DM) halos. This shape
can be reproduced well by a density profile with a shallow central cusp
(rho(r)\propto 1/r^gamma, gamma\approx 0.2-0.4), corresponding to a steeply
rising velocity curve (v(r)\propto r^g, g\approx 0.9-0.8). We further show that
the observed shape of the rotation curves is well matched by the density
profiles of DM halos formed in very high resolution simulations of the CDM,
LCDM, and CHDM models of structure formation. This is surprising in light of
several previous studies which suggested that the structure of simulated DM
halos is inconsistent with the dynamics of dwarf galaxies. We discuss possible
explanations for this discrepancy. We show that although the mass distribution
in the hierarchically formed halos is on average consistent with the shape of
rotation curves of dark matter dominated galaxies, the scatter of the
individual profiles around the average is substantial and should not be
neglected in comparisons with the data. Finally, we show that the DM halos in
our hierarchical simulations and the real galaxies in our sample exhibit a
similar decrease in their characteristic densities with increasing
characteristic radial scales, and increase in their maximum rotation velocities
with increasing radii at which their maximum velocity occurs. (Abridged)
