We present high-resolution optical spectra of 15 objects near or below the substellar limit in the Upper Scorpius and ρ Ophiuchus star-forming regions. These spectra, obtained with the High Resolution Echelle Spectrometer on the Keck I telescope, are used to investigate disk accretion, rotation, and activity in young very low mass objects. We report the detection of a broad, asymmetric Hα emission line in the ρ Oph source GY 5, which is also known to harbor mid-infrared excess, consistent with the presence of an accreting disk. The Hα profiles of the Upper Sco objects suggest little or no ongoing accretion. Our results imply that if most brown dwarfs are born with disks, their accretion rates decrease rapidly, at timescales comparable to or smaller than those for T Tauri disks. The Upper Sco brown dwarfs appear to be rotating faster than their somewhat younger counterparts in Taurus, consistent with spin-up due to contraction following disk unlocking. The Hα activity is comparable to saturated activity levels in field M dwarfs with similar spectral type and rotation rates. Comparison of our data with published (albeit lower resolution) spectra of a few of the same objects from other epochs suggests possible variability in accretion/activity indicators.