We present a study of accretion in a sample of 45 young, low mass objects in a variety of star forming regions and young associations, about half of which are likely substellar. Based primarily on the presence of broad, asymmetric Halpha emission, we have identified 13 objects (~30% of our sample) which are strong candidates for ongoing accretion. At least 3 of these are substellar. We do not detect significant continuum veiling in most of the accretors with late spectral types (M5-M7). Accretion shock models show that lack of measurable veiling allows us to place an upper limit to the mass accretion rates of

38 pages, including 8 figures and 6 tables, accepted by ApJ