  The present experimental status does not exclude weak-strength non-standard
interactions of neutrinos with electrons. These interactions can be revealed in
solar neutrino experiments. Our discussion covers several aspects related to
this issue. First, we perform an analysis of the Super Kamiokande and SNO data
to investigate their sensitivity to such interactions. In particular, we show
that the \nu_e oscillation into sterile neutrinos can be still allowed if \nu_e
has extra interactions of the proper strength. Second, we suggest that the
Borexino detector can provide good signatures for these non-standard
interactions. Indeed, in Borexino the shape of the recoil electron spectrum
from the \nu e \to \nu e scattering essentially does not depend on the solar
neutrino conversion details, since most of the signal comes from the
mono-energetic ^7Be neutrinos. Hence, the partial conversion of solar \nu_e
into a a nearly equal mixture of \nu_\mu and \nu_\tau, as is indicated by the
atmospheric neutrino data, offers the chance to test extra interactions of
\nu_\tau, or of \nu_e itself.
