  We study phase transitions in the two-dimensional Heisenberg model with the
Dzyaloshinskii-Moriya interaction, the Ising anisotropy ($\eta$), and the
dipolar interaction under zero and finite magnetic fields ($H$). For three
typical strengths (zero, weak, and strong) of the dipolar interaction, we
present the $H$-$\eta$ phase diagrams by estimating order parameters for
skyrmion-lattice and helical phases and in-plane magnetization by using a Monte
Carlo method with an $O(N)$ algorithm. We find in the phase diagrams three
types of skyrmion-lattice phases, i.e., two square lattices and a triangular
lattice, helical phases with diagonal and vertical (or horizontal) stripes,
canted ferromagnetic phase and polarized ferromagnetic phase. The effect of the
dipolar interaction varies the types of the skyrmion and helical phases in a
complex manner. The dipolar interaction also expands the regions of the ordered
phases accompanying shifts of the phase boundaries to the positive $H$ and
$\eta$ directions, and causes increase of the density of skyrmions and
shortening of the pitch length (stripe width) of helical structures. We discuss
the details of the features of the phase transitions.
