  We show that Jastrow-Slater wave functions, in which a density-density
Jastrow factor is applied onto an uncorrelated fermionic state, may possess
long-range order even when all symmetries are preserved in the wave function.
This fact is mainly related to the presence of a sufficiently strong Jastrow
term (also including the case of full Gutzwiller projection, suitable for
describing spin models). Selected examples are reported, including the spawning
of N\'eel order and dimerization in spin systems, and the stabilization of
charge and orbital order in itinerant electronic systems.
