We describe measurements of GeV and TeV cosmic rays with the High-Altitude Water Cherenkov Gamma-Ray Observatory, or HAWC. The measurements include the observation of the shadow of the moon; the observation of small-scale and large-scale angular clustering of the TeV cosmic rays; the prospects for measurement of transient solar events with HAWC; and the observation of Forbush decreases with the HAWC engineering array and HAWC-30.