We introduce EigenRec; a versatile and efficient Latent-Factor framework for Top-N Recommendations that includes the well-known PureSVD algorithm as a special case. EigenRec builds a low dimensional model of an inter-item proximity matrix that combines a similarity component, with a scaling operator, designed to control the influence of the prior item popularity on the final model. Seeing PureSVD within our framework provides intuition about its inner workings, exposes its inherent limitations, and also, paves the path towards painlessly improving its recommendation performance. A comprehensive set of experiments on the MovieLens and the Yahoo datasets based on widely applied performance metrics, indicate that EigenRec outperforms several state-of-the-art algorithms, in terms of Standard and Long-Tail recommendation accuracy, exhibiting low susceptibility to sparsity, even in its most extreme manifestations -- the Cold-Start problems. At the same time EigenRec has an attractive computational profile and it can apply readily in large-scale recommendation settings.