ABSTRACT We present a new model for the distribution of free electrons in the Galaxy, the Magellanic Clouds, and the intergalactic medium (IGM) that can be used to estimate distances to real or simulated pulsars and fast radio bursts (FRBs) based on their dispersion measure (DM). The Galactic model has an extended thick disk representing the so-called warm interstellar medium, a thin disk representing the Galactic molecular ring, spiral arms based on a recent fit to Galactic H ii regions, a Galactic Center disk, and seven local features including the Gum Nebula, Galactic Loop I, and the Local Bubble. An offset of the Sun from the Galactic plane and a warp of the outer Galactic disk are included in the model. Parameters of the Galactic model are determined by fitting to 189 pulsars with independently determined distances and DMs. Simple models are used for the Magellanic Clouds and the IGM. Galactic model distances are within the uncertainty range for 86 of the 189 independently determined distances and within 20% of the nearest limit for a further 38 pulsars. We estimate that 95% of predicted Galactic pulsar distances will have a relative error of less than a factor of 0.9. The predictions of YMW16 are compared to those of the TC93 and NE2001 models showing that YMW16 performs significantly better on all measures. Timescales for pulse broadening due to interstellar scattering are estimated for (real or simulated) Galactic and Magellanic Cloud pulsars and FRBs.