  Motivated by recent developments in string theory, we study the structure of
boundary conditions in arbitrary conformal field theories. A boundary condition
is specified by two types of data: first, a consistent collection of reflection
coefficients for bulk fields on the disk; and second, a choice of an
automorphism $\omega$ of the fusion rules that preserves conformal weights.
Non-trivial automorphisms $\omega$ correspond to D-brane configurations for
arbitrary conformal field theories. The choice of the fusion rule automorphism
$\omega$ amounts to fixing the dimension and certain global topological
features of the D-brane world volume and the background gauge field on it. We
present evidence that for fixed choice of $\omega$ the boundary conditions are
classified as the irreducible representations of some commutative associative
algebra, a generalization of the fusion rule algebra. Each of these irreducible
representations corresponds to a choice of the moduli for the world volume of
the D-brane and the moduli of the flat connection on it.
