Let Ω be a domain in \mathbb{R}^{n} or a noncompact Riemannian manifold of dimension n \geq 2 , and 1 < p < \infty . Consider the functional \mathcal{Q}(\varphi ): = \int _{\Omega }(|\mathrm{∇}\varphi |^{p} + V|\varphi |^{p})\:\mathrm{d}\nu defined on C_{0}^{\infty }(\Omega ) , and assume that \mathcal{Q} \geq 0 . The aim of the paper is to generalize to the quasilinear case ( p \neq 2 ) some of the results obtained in [6] for the linear case ( p = 2 ), and in particular, to obtain “as large as possible” nonnegative (optimal) Hardy-type weight W satisfying \mathcal{Q}(\varphi ) \geq \int \limits_{\Omega }W|\varphi |^{p}\:\mathrm{d}\nu \:\forall \varphi \in C_{0}^{\infty }(\Omega ). Our main results deal with the case where V = 0 , and Ω is a general punctured domain (for V \neq 0 we obtain only some partial results). In the case 1 < p \leq n , an optimal Hardy-weight is given by W: = \left(\frac{p−1}{p}\right)^{p}\left|\frac{\mathrm{∇}G}{G}\right|^{p}, where G is the associated positive minimal Green function with a pole at 0 . On the other hand, for p > n , several cases should be considered, depending on the behavior of G at infinity in Ω . The results are extended to annular and exterior domains.