  We study critical behavior in the collapse of massive spherically symmetric
scalar fields. We observe two distinct types of phase transition at the
threshold of black hole formation. Type II phase transitions occur when the
radial extent $(\lambda)$ of the initial pulse is less than the Compton
wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that
found by Choptuik in the collapse of massless scalar fields. Type I phase
transitions, where the black hole formation turns on at finite mass, occur when
$\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with
masses $\alt 0.6 \mu^{-1}$. Our results in combination with those obtained for
the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon,
Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to
the Einstein-matter equations may be relevant to the critical point of other
matter models.
