  This paper presents a post-Newtonian (PN) template family of gravitational
waveforms from inspiralling compact binaries with non-precessing spins, where
the spin effects are described by a single "reduced-spin" parameter. This
template family, which reparametrizes all the spin-dependent PN terms in terms
of the leading-order (1.5PN) spin-orbit coupling term \emph{in an approximate
way}, has very high overlaps (fitting factor > 0.99) with non-precessing
binaries with arbitrary mass ratios and spins. We also show that this template
family is "effectual" for the detection of a significant fraction of generic
spinning binaries in the comparable-mass regime (m_2/m_1 <~ 10), providing an
attractive and feasible way of searching for gravitational waves (GWs) from
spinning low-mass binaries. We also show that the secular (non-oscillatory)
spin-dependent effects in the phase evolution (which are taken into account by
the non-precessing templates) are more important than the oscillatory effects
of precession in the comparable-mass (m_1 ~= m_2) regime. Hence the
effectualness of non-spinning templates is particularly poor in this case, as
compared to non-precessing-spin templates. For the case of binary neutron stars
observable by Advanced LIGO, even moderate spins (L . S/m^2 ~= 0.015 - 0.1)
will cause considerable mismatches (~ 3% - 25%) with non-spinning templates.
This is contrary to the expectation that neutron-star spins may not be relevant
for GW detection.
