© 2014. The American Astronomical Society. All rights reserved.. We analyze Mg II λλ2796, 2803 and Fe II λλ2586, 2600 absorption profiles in individual spectra of 105 galaxies at 0.3 < z < 1.4. The galaxies, drawn from redshift surveys of the GOODS fields and the Extended Groth Strip, sample the range in star formation rates (SFRs) occupied by the star-forming sequence with stellar masses log M ∗/M ≳ 9.6 down to SFR ≳ 2 M yr-1 at 0.3 < z < 0.7. Using the Doppler shifts of Mg II and Fe II absorption as tracers of cool gas kinematics, we detect large-scale winds in 66 ± 5% of the galaxies. Hubble Space Telescope Advanced Camera for Surveys imaging and our spectral analysis indicate that the outflow detection rate depends primarily on galaxy orientation: winds are detected in ∼89% of galaxies having inclinations (i) <30° (face-on), while the wind detection rate is ∼45% in objects having i > 50° (edge-on). Combined with the comparatively weak dependence of wind detection rate on intrinsic galaxy properties, this implies that biconical outflows are ubiquitous in normal, star-forming galaxies at z ∼ 0.5. We find that wind velocity is correlated with galaxy M ∗ at 3.4σ significance, while outflow equivalent width is correlated with SFR at 3.5σ significance, suggesting hosts with higher SFR launch more material and/or generate a larger velocity spread for the absorbing clouds. Assuming the gas is driven into halos with isothermal density profiles, the wind velocities (∼200-400 km s-1) permit escape from the halo potentials only for the lowest-M ∗ systems in the sample. However, the gas carries sufficient energy to reach distances ≳ 50 kpc, and may therefore be a viable source of material for the massive, cool circumgalactic medium around bright galaxies at z ∼ 0.