Transition metal carbides are a class of materials widely known for both their interesting physical properties and catalytic activity. In this work, we have used plane-wave DFT methods to study the interaction with increasing amounts of molecular hydrogen on the low-index surfaces of four major carbides - TiC, VC, ZrC and NbC. Adsorption is found to be generally exothermic and occurs predominantly on the surface carbon atoms. We identify trends over the carbides and their surfaces for the energetics of the adsorption as a function of their electronic and geometrical characteristics. An ab initio thermodynamics formalism is used to study the properties of the slabs as the hydrogen coverage is increased.