A theoretical evaluation of the thermoelectric-related electrical transport properties of 36 half-Heusler (HH) compounds, selected from more than 100 HHs, is carried out in this paper. The electronic structures and electrical transport properties are studied using ab initio calculations and the Boltzmann transport equation under the constant relaxation time approximation for charge carriers. The electronic structure results predict the band gaps of these HH compounds, and show that many HHs are narrow-band-gap semiconductors and, therefore, are potentially good thermoelectric materials. The dependence of Seebeck coefficient, electrical conductivity, and power factor on the Fermi level is investigated. Maximum power factors and the corresponding optimal p- or n-type doping levels, related to the thermoelectric performance of materials, are calculated for all HH compounds investigated, which certainly provide guidance to experimental work. The estimated optimal doping levels and Seebeck coefficients show reasonable agreement with the measured results for some HH systems. A few HHs are recommended to be potentially good thermoelectric materials based on our calculations.