  We analyze the set of magnetic charges carried by smooth BPS monopoles in
Yang-Mills-Higgs theory with arbitrary gauge group G spontaneously broken to a
subgroup H. The charges are restricted by a generalized Dirac quantization
condition and by an inequality due to Murray. Geometrically, the set of allowed
charges is a solid cone in the coroot lattice of G, which we call the Murray
cone. We argue that magnetic charge sectors correspond to points in the Murray
cone divided by the Weyl group of H; hence magnetic charge sectors are labelled
by dominant integral weights of the dual group H*. We define generators of the
Murray cone modulo Weyl group, and interpret the monopoles in the associated
magnetic charge sectors as basic; monopoles in sectors with decomposable
charges are interpreted as composite configurations. This interpretation is
supported by the dimensionality of the moduli spaces associated to the magnetic
charges and by classical fusion properties for smooth monopoles in particular
cases. Throughout the paper we compare our findings with corresponding results
for singular monopoles recently obtained by Kapustin and Witten.
