This paper presents the gravitational-wave measurement of the Hubble constant ($H_0$) using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standard-siren measurement of $H_0$. Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is $H_0 = 68.7^{+17.0}_{-7.8}$ km/s/Mpc (68.3\% of the highest density posterior interval with a flat-in-log prior) which is an improvement by a factor of 1.04 (about 4\%) over the GW170817-only value of $68.7^{+17.5}_{-8.3}$ km/s/Mpc. A significant additional contribution currently comes from GW170814, a loud and well-localized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years, an exhaustive understanding of other systematic effects are also going to become increasingly important. These results establish the path to cosmology using gravitational-wave observations with and without transient electromagnetic counterparts.