  We present new L-band ($1\mbox{--}2$ GHz) observations of the nearby spiral
galaxy M33 with 80 pc resolution obtained with the Karl G. Jansky Very Large
Array. The HI observations, combined with HI measurements from the Green Bank
Telescope, improve the spectral resolution and sensitivity ($2.8$ K rms noise
in a $0.2$ km s$^{-1}$ channel) compared to previous observations. We find
individual profiles are usually non-Gaussian, harbouring line wings, multiple
components, and asymmetries. Given this spectral complexity, we quantify the
motions in the atomic ISM through moment analysis of the spectra and fits to
aligned, stacked profiles. The measured value of the HI line width depends
strongly on the method used, with the velocity stacked profiles aligned to the
peak velocity giving the minimum value of $\sigma = 7$ km s$^{-1}$ and all
other methods giving higher values ($\sigma\sim10$ km s$^{-1}$). All
measurements of the line width show a shallow radial trend, with $\sigma$
decreasing by $\sim2$ km s$^{-1}$ from $R_{\rm gal}=0$ to $R_{\rm gal}=8$ kpc.
We consider a number of energy sources that might maintain the line width
against turbulent dissipation, but no single source is adequate. We find excess
emission relative to a Gaussian in the stacked profile line wings, ranging from
9% to 26% depending on how the spectra are aligned. By splitting the line wings
into symmetric and asymmetric components, we find that the lagging rotational
disk accounts for one-third of the line wing flux. We also find emission far
from the rotation axis of the galaxy in multiple discrete HI clouds, including
a filament with a projected length of $\sim8$ kpc.
