  We study boundary conditions for the bosonic, spinning (NSR) and
Green-Schwarz open string, as well as for 1+1 dimensional supergravity. We
consider boundary conditions that arise from (1) extremizing the action, (2)
BRST, rigid or local supersymmetry, or kappa(Siegel)-symmetry of the action,
(3) closure of the set of boundary conditions under the symmetry
transformations, and (4) the boundary limits of bulk Euler-Lagrange equations
that are ``conjugate'' to other boundary conditions. We find corrections to
Neumann boundary conditions in the presence of a bulk tachyon field. We discuss
a boundary superspace formalism. We also find that path integral quantization
of the open string requires an infinite tower of boundary conditions that can
be interpreted as a smoothness condition on the doubled interval; we interpret
this to mean that for a path-integral formulation of open strings with only
Neumann boundary conditions, the description in terms of orientifolds is not
just natural, but is actually fundamental.
