We describe AEGIS20-a radio survey of the Extended Groth Strip (EGS) conducted with the Very Large Array (VLA) at 1.4 GHz. The resulting catalog contains 1123 emitters and is sensitive to ultraluminous (10^12 L⊙) starbursts to z ≤ 1.3, well matched to the redshift range of the DEEP2 spectroscopic survey in this region. We use stacking techniques to explore the microjansky-level emission from a variety of galaxy populations selected via conventional criteria-Lyman break galaxies (LBGs), distant red galaxies (DRGs), UV-selected galaxies, and extremely red objects (EROs)-determining their properties as a function of color, magnitude, and redshift and their extinction-free contributions to the history of star formation. We confirm the familiar pattern that the star formation rate (SFR) density, ρ_*, increases by at least a factor of ~5 from z = 0 to 1, although we note highly discrepant UV- and radio-based SFR estimates. Our radio-based SFRs become more difficult to interpret at z > 1 where correcting for contamination by radio-loud active galactic nuclei (AGNs) comes at the price of rejecting luminous starbursts. While stacking radio images is a useful technique, accurate radio-based SFRs for z » 1 galaxies require precise redshifts and extraordinarily high fidelity radio data to identify and remove accretion-related emission