  We analyze the scalar potentials of maximal gauged three-dimensional
supergravities which reveal a surprisingly rich structure. In contrast to
maximal supergravities in dimensions D>3, all these theories admit a maximally
supersymmetric (N=16) ground state with negative cosmological constant
Lambda<0, except for the gauge group SO(4,4)^2, for which Lambda=0. We compute
the mass spectra of bosonic and fermionic fluctuations around these vacua and
identify the unitary irreducible representations of the relevant background
(super)isometry groups to which they belong. In addition, we find several
stationary points which are not maximally supersymmetric, and determine their
complete mass spectra as well. In particular, we show that there are analogs of
all stationary points found in higher dimensions, among them de Sitter vacua in
the theories with noncompact gauge groups SO(5,3)^2 and SO(4,4)^2, as well as
anti-de Sitter vacua in the compact gauged theory preserving 1/4 and 1/8 of the
supersymmetries. All the dS vacua have tachyonic instabilities, whereas there
do exist non-supersymmetric AdS vacua which are stable, again in contrast to
the D>3 theories.
