Neural Radiance Fields (NeRFs) have achieved impressive results in novel view synthesis and surface reconstruction tasks. However, their performance suffers under challenging scenarios with sparse input views. We present CorresNeRF, a novel method that leverages image correspondence priors computed by off-the-shelf methods to supervise NeRF training. We design adaptive processes for augmentation and filtering to generate dense and high-quality correspondences. The correspondences are then used to regularize NeRF training via the correspondence pixel reprojection and depth loss terms. We evaluate our methods on novel view synthesis and surface reconstruction tasks with density-based and SDF-based NeRF models on different datasets. Our method outperforms previous methods in both photometric and geometric metrics. We show that this simple yet effective technique of using correspondence priors can be applied as a plug-and-play module across different NeRF variants. The project page is at https://yxlao.github.io/corres-nerf/.