We analyze the rapid, aperiodic X-ray variability of different types of X-r
ay binaries (black hole candidates, atoll sources, the recently discovered
millisecond X-ray pulsar, and Z sources) at their lowest inferred mass accr
etion rates. At these accretion rates, the power spectra of all sources are
dominated by a strong band-limited noise component, which follows a power
law with an index of roughly 1 at high frequencies and breaks at a frequenc
y between 0.02 and 32 Hz, below which the spectrum is relatively flat. Supe
rimposed on this, a broad bump (sometimes a quasi-periodic oscillation) is
present, with a 0.2-67 Hz centroid frequency that varies in good correlatio
n with the frequency of the break. The black hole candidates and the low-lu
minosity neutron star systems (including the millisecond X-ray pulsar) have
the same relation between the frequency of the bump and the frequency of t
he break. These similar characteristics strongly suggest that in all those
different types of sources, the band-limited noise and the bump are produce
d by the same physical mechanism. This mechanism cannot then depend on the
presence or absence of either a small magnetosphere or a solid surface, so
that it is most likely related to an instability in the flow in the accreti
on disk that modulates the accretion rate. The Z sources, which are more lu
minous than the other sources discussed here, follow a similar, but slightl
y shifted correlation between the break frequency and the frequency of the
bump. The data suggest that the band-limited noise in Z sources is more com
plex than that in the other sources.