We show how three-dimensional superconformal theories for any number N <= 8
of supersymmetries can be obtained by taking a conformal limit of the
corresponding three-dimensional gauged supergravity models. The superconformal
theories are characterized by an embedding tensor that satisfies a linear and
quadratic constraint. We analyze these constraints and give the general
solutions for all cases. We find new N = 4,5 superconformal theories based on
the exceptional Lie superalgebras F(4), G(3) and D(2|1;\alpha). Using the
supergravity connection we discuss which massive deformations to expect. As an
example we work out the details for the case of N = 6 supersymmetry.Comment: 22 pages; v2: refs. added, minor corrections, version published in
JHE