Using the brick wall regularization of 't Hooft, the entropy of non-extreme and extreme black holes is investigated in a general static, spherically symmetric spacetime. We classify the singularity in the entropy by introducing a new index δ with respect to the brick wall cut-off ϵ. The leading contribution to entropy for the non-extreme case (δ ≠ 0) is shown to satisfy the area law with quadratic divergence with respect to the invariant cut-off ϵinv while the extreme case (δ = 0) exhibits logarithmic divergence or constant value with respect to ϵ. The general formula is applied to Reissner–Nordström, dilaton and brane-world black holes and we obtain consistent results.