  We study order-parameter fluctuations (OPF) in disordered systems by
considering the behavior of some recently introduced paramaters $G,G_c$ which
have proven very useful to locate phase transitions. We prove that both
parameters G (for disconnected overlap disorder averages) and $G_c$ (for
connected disorder averages) take the respective universal values 1/3 and 13/31
in the $T\to 0$ limit for any {\em finite} volume provided the ground state is
{\em unique} and there is no gap in the ground state local-field distributions,
conditions which are met in generic spin-glass models with continuous couplings
and no gap at zero coupling. This makes $G,G_c$ ideal parameters to locate
phase transitions in disordered systems much alike the Binder cumulant is for
ordered systems. We check our results by exactly computing OPF in a simple
example of uncoupled spins in the presence of random fields and the
one-dimensional Ising spin glass. At finite temperatures, we discuss in which
conditions the value 1/3 for G may be recovered by conjecturing different
scenarios depending on whether OPF are finite or vanish in the infinite-volume
limit. In particular, we discuss replica equivalence and its natural
consequence $\lim_{V\to\infty}G(V,T)=1/3$ when OPF are finite. As an example of
a model where OPF vanish and replica equivalence does not give information
about G we study the Sherrington-Kirkpatrick spherical spin-glass model by
doing numerical simulations for small sizes. Again we find results compatible
with G=1/3 in the spin-glass phase.
