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The segmentation of the retinal vasculature from eye fundus images represents one of the most fundamental tasks in retinal image analysis. Over recent years, increasingly complex approaches based on sophisticated Convolutional Neural Network architectures have been slowly pushing performance on well-established benchmark datasets. In this paper, we take a step back and analyze the real need of such complexity. Specifically, we demonstrate that a minimalistic version of a standard U-Net with several orders of magnitude less parameters, carefully trained and rigorously evaluated, closely approximates the performance of current best techniques. In addition, we propose a simple extension, dubbed W-Net, which reaches outstanding performance on several popular datasets, still using orders of magnitude less learnable weights than any previously published approach. Furthermore, we provide the most comprehensive cross-dataset performance analysis to date, involving up to 10 different databases. Our analysis demonstrates that the retinal vessel segmentation problem is far from solved when considering test images that differ substantially from the training data, and that this task represents an ideal scenario for the exploration of domain adaptation techniques. In this context, we experiment with a simple self-labeling strategy that allows us to moderately enhance cross-dataset performance, indicating that there is still much room for improvement in this area. Finally, we also test our approach on the Artery/Vein segmentation problem, where we again achieve results well-aligned with the state-of-the-art, at a fraction of the model complexity in recent literature. All the code to reproduce the results in this paper is released.