Radiolysis of water with radioactive rocks
(H2O → H2, H2O2 plus various ions)

Serpentinisation of mafic rocks
(Fe + H2O = Fe2O4 + H2)

Anaerobic digestion with H2 being generated as part of the breakdown of organic matter.

Over maturing hydrocarbon source rocks generates H2

Cataclasis: crushing silica in the presence of water.
(Si + H2O = SiO2 + H2)

Degassing of the earth could generate a continuous flux of H2