Using the largest high-resolution spectroscopic sample to date of young, very low mass stars and brown dwarfs, we investigate disk accretion in objects ranging from just above the hydrogen-burning limit all the way to nearly planetary masses. Our 82 targets span spectral types from M5 to M9.5, or masses from 0.15 M down to about 15 jupiters. They are confirmed members of the ρ Ophiuchus, Taurus, Chamaeleon I, IC 348, R Coronae Australis, Upper Scorpius, and TW Hydrae star-forming regions and young clusters, with ages from <1 to ~10 Myr. The sample contains 41 brown dwarfs (spectral types ≥M6.5). We have previously presented high-resolution optical spectra for roughly half the sample; the rest are new. This is a close to complete survey of all confirmed brown dwarfs known so far in the regions examined, except in ρ Oph and IC 348 (where we are limited by a combination of extinction and distance). We find that (1) classical T Tauri-like disk accretion persists in the substellar domain down to nearly the deuterium-burning limit; (2) while an Hα 10% width 200 km s^-1 is our prime accretion diagnostic (following our previous work), permitted emission lines of Ca II, O I, and He I are also good accretion indicators, just as in classical T Tauri stars (we caution against a blind use of Hα width alone, since inclination and rotation effects on the line are especially important at the low accretion rates in very low mass objects); (3) the Ca II λ8662 line flux is an excellent quantitative measure of the accretion rate in very low mass stars and brown dwarfs (as in higher mass classical T Tauri Stars), correlating remarkably well with the obtained from veiling and Hα modeling; (4) the accretion rate diminishes rapidly with mass—our measurements support previous suggestions that (albeit with considerable scatter) and extend this correlation to the entire range of substellar masses; (5) the fraction of very low mass stellar and substellar accretors decreases substantially with age, as in higher mass stars; (6) at any given age, the fraction of very low mass stellar and substellar accretors is comparable to the accretor fraction in higher mass stars; and (7) a number of our sources with infrared excesses arising from dusty disks do not evince measurable accretion signatures, with the incidence of such a mismatch increasing with age: this implies that disks in the low-mass regime can persist beyond the main accretion phase and parallels the transition from the classical to post-T Tauri stage in more massive stars. These strong similarities at young ages, between higher mass stars on the one hand and low-mass bodies close to and below the hydrogen-burning limit on the other, are consistent with a common formation mechanism in the two mass regimes.