We construct two new classes of exact solutions to string theory which
are not of the standard plane wave or gauged WZW type. Many of these
solutions have curvature singularities. The first class includes the f
undamental string solution, for which the string coupling vanishes nea
r the singularity. This suggests that the singularity may not be remov
ed by quantum corrections. The second class consists of hybrids of pla
ne wave and gauged WZW solutions. We discuss a four-dimensional exampl
e in detail.