Which superpositions are allowed or forbidden in principle is determined by so-called superselection sectors. http://en.wikipedia.org/wiki/Superselection
These are virtually absent from the standard textbook literature as they cannot be inferred from the traditional perturbative treatment of quantum mechanics or quantum field theory.
The superselection rule easiest to understand is the one that forbids the superpositions of a boson state and a fermion state. The reason is that these states transform differently under the action of the rotation group, hence there is no consistent action of the rotation group on the superposition. (Under a 360 degree rotation The boson half would rotate back to itself, while the fermion half changes its sign.)
This shows that superselection rules are tied to inequivalent representation of Lie groups or Lie algebras of quantities defining the physics of a system. The charge superselection rule is associated to inequivalent representations of an infinite-dimensional Heisenberg group defining the canonical commutation relations (CCR) of a relativistic quantum field. [My discussion assumes the bosonic case. In case of fermions, one needs instead the CAR, and s similar reasoning applies.]
Here the reasoning is more intricate, and requires the nonperturbative setting of algebraic quantum field theory. In this setting, observables form a C^*-algebra, and states are suitable positive linear functionals of this algebra.
The analogous standard QM situation is where the C^*-algebra is the algebra of bounded linear operators on a Hilbert space, and a state is the expectation mapping $\langle A\rangle =Tr ~\rho A$ with a positive semidefinite density matrix $\rho$ of trace 1. Here the uniqueness theorem of von Neumann guarantees that the canonical commutation relations have a unique unitary representation up to unitary equivalence.
However, this theorem only holds for CCR of finitely many operators, whereas field theory deals with infinitely many of these. The CCR of field theory have infinitely many inequivalent representations, and these live in different Hilbert spaces, between the elements of which no sensible inner product is defined. As it makes no sense to consider superpositions between states of two different Hilbert spaces (not embedded in a common Hilbert space with a physical meaning), inequivalent representations imply a superselection rule.
This implies the charge superselection rule for QED, as it can be shown that in QED, states of different charge must lie in inequivaent representations.