  "High-velocity features" (HVFs) are spectral features in Type Ia supernovae
(SNe Ia) that have minima indicating significantly higher (by greater than
about 6000 km/s) velocities than typical "photospheric-velocity features"
(PVFs). The PVFs are absorption features with minima indicating typical
photospheric (i.e., bulk ejecta) velocities (usually ~9000-15,000 km/s near
B-band maximum brightness). In this work we undertake the most in-depth study
of HVFs ever performed. The dataset used herein consists of 445 low-resolution
optical and near-infrared (NIR) spectra (at epochs up to 5 d past maximum
brightness) of 210 low-redshift SNe Ia that follow the "Phillips relation." A
series of Gaussian functions is fit to the data in order to characterise
possible HVFs of Ca II H&K, Si II {\lambda}6355, and the Ca II NIR triplet. The
temporal evolution of the velocities and strengths of the PVFs and HVFs of
these three spectral features is investigated, as are possible correlations
with other SN Ia observables. We find that while HVFs of Ca II are regularly
observed (except in underluminous SNe Ia, where they are never found), HVFs of
Si II {\lambda}6355 are significantly rarer, and they tend to exist at the
earliest epochs and mostly in objects with large photospheric velocities. It is
also shown that stronger HVFs of Si II {\lambda}6355 are found in objects that
lack C II absorption at early times and that have red ultraviolet/optical
colours near maximum brightness. These results lead to a self-consistent
connection between the presence and strength of HVFs of Si II {\lambda}6355 and
many other mutually correlated SN~Ia observables, including photospheric
velocity.
