Unsupervised video object segmentation has often been tackled by methods based on recurrent neural networks and optical flow. Despite their complexity, these kinds of approach tend to favour short-term temporal dependencies and are thus prone to accumulating inaccuracies, which cause drift over time. Moreover, simple (static) image segmentation models, alone, can perform competitively against these methods, which further suggests that the way temporal dependencies are modelled should be reconsidered. Motivated by these observations, in this paper we explore simple yet effective strategies to model long-term temporal dependencies. Inspired by the non-local operators of Xiaolong Wang et al. (CVPR 2018), we introduce a technique to establish dense correspondences between pixel embeddings of a reference "anchor" frame and the current one. This allows the learning of pairwise dependencies at arbitrarily long distances without conditioning on intermediate frames. Without online supervision, our approach can suppress the background and precisely segment the foreground object even in challenging scenarios, while maintaining consistent performance over time. With a mean IoU of 81.7%, our method ranks first on the DAVIS-2016 leaderboard of unsupervised methods, while still being competitive against state-of-the-art online semi-supervised approaches. We further evaluate our method on the FBMS dataset and the video saliency dataset ViSal, showing results competitive with the state of the art.