The classical Green-Schwarz superstring action, with N=1 or N=2 spacetime
supersymmetry, exists for spacetime dimensions D=3,4,6,10, but quantization in
the light-cone gauge breaks Lorentz invariance unless either D=10, which leads
to critical superstring theory, or D=3. We give details of results presented
previously for the bosonic and N=1 closed 3D (super)strings and extend them to
the N=2 3D superstring. In all cases, the spectrum is parity-invariant and
contains anyons of irrational spin.Comment: 46 pages, v5 corrects more typos and minor error
