  We consider random walks associated with conductances on Delaunay
triangulations, Gabriel graphs and skeletons of Voronoi tilings which are
generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on
point processes and conductances, we show that, for almost any realization of
the point process, these random walks are recurrent if $d=2$ and transient if
$d\geq 3$. These results hold for a large variety of point processes including
Poisson point processes, Mat{\'e}rn cluster and Mat{\'e}rn hardcore processes
which have clustering or repulsive properties. In order to prove them, we state
general criteria for recurrence or almost sure transience which apply to random
graphs embedded in $\mathbb{R}^d$.
