We investigate galactic-scale outflowing winds in 72 star-forming galaxies at z~1 in the Extended Groth Strip. Galaxies were selected from the DEEP2 survey and follow-up LRIS spectroscopy was obtained covering SiII, CIV, FeII, MgII, and MgI lines in the rest-frame ultraviolet. Using GALEX, HST, and Spitzer imaging, we examine galaxies on a per-object basis in order to understand both the prevalence of galactic winds at z~1 and the star-forming and structural properties of objects experiencing outflows. Gas velocities, measured from the centroids of FeII interstellar absorption lines, span the interval [-217, +155] km/s. We find that ~40% (10%) of the sample exhibits blueshifted FeII lines at the 1-sigma (3-sigma) level. We also measure maximal outflow velocities using the profiles of the FeII and MgII lines, and show that MgII frequently traces higher velocity gas than FeII. Quantitative morphological parameters derived from the HST imaging suggest that mergers are not a prerequisite for driving outflows. More face-on galaxies also show stronger winds than highly-inclined systems, consistent with the canonical picture of winds emanating perpendicular to galactic disks. Using star-formation rates calculated from GALEX data, and areas estimated from HST imaging, we detect a ~3-sigma correlation between outflow velocity and star-formation rate surface density, but only a weak (~1-sigma) trend between outflow velocity and star-formation rate. Higher resolution data are needed in order to test the scaling relations between outflow velocity and both star-formation rate and star-formation rate surface density predicted by theory.