  We construct a class of exactly solvable generalized Kitaev spin-$1/2$ models
in arbitrary dimensions, which is beyond the category of quantum compass
models. The Jordan-Wigner transformation is employed to prove the exact
solvability. An exactly solvable quantum spin-$1/2$ models can be mapped to a
gas of free Majorana fermions coupled to static $Z_2$ gauge fields. We classify
these exactly solvable models according to their parent models. Any model
belonging to this class can be generated by one of the parent models. For
illustration, a two dimensional ($2D$) tetragon-octagon model and a three
dimensional ($3D$) $xy$ bond model are studied.
