In this paper, stochastic interval Hopfield neural networks with time-varying delays are investigated. By applying the Razumikhin-type theorem as well as inequality technique, a set of novel sufficient criteria independent of delays are given for the exponential stability of such networks. As a by-product, for the deterministic Hopfield neural networks with time-varying delays, some delay-independent criteria for their global exponential robust stability are also obtained. The proposed results improve and extend them in the earlier literature and are easier to verify. A numerical example and simulation are also given to illustrate the effectiveness of our results.