  As a candidate of quantum gravity in ultrahigh energy, the
$(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent
$z\ne 1$, indicates anisotropy between time and space at short distance. In the
paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in
arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter
$\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary
dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we
study the topological neutral black hole solutions with general $\lambda$ in
$z=d$ HL$_{d+1}$, as well as the topological charged black holes with
$\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation
is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De
Witt's canonical gravity with $\lambda=1$. In particular, the topological
charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$
HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the
infinite boundary and near the horizon are explored respectively. We also study
the behavior of the topological black holes in the $(d+1)$-dimensional HL
gravity with $U(1)$ gauge field in the zero temperature limit and finite
temperature limit, respectively. Thermodynamics of the topological charged
black holes with $\lambda=1$, including temperature, entropy, heat capacity,
and free energy are evaluated.
