Small non-coding RNAs (sncRNAs) are highly abundant molecules that regulate essential cellular processes and are classified according to sequence and structure. Here we argue that read profiles from size-selected RNA sequencing capture the post-transcriptional processing specific to each RNA family, thereby providing functional information independently of sequence and structure. We developed SeRPeNT, a new computational method that exploits reproducibility across replicates and uses dynamic time-warping and density-based clustering algorithms to identify, characterize and compare sncRNAs by harnessing the power of read profiles. We applied SeRPeNT to: (i) generate an extended human annotation with 671 new sncRNAs from known classes and 131 from new potential classes, (ii) show pervasive differential processing of sncRNAs between cell compartments and (iii) predict new molecules with miRNA-like behaviour from snoRNA, tRNA and long non-coding RNA precursors, potentially dependent on the miRNA biogenesis pathway. Furthermore, we validated experimentally four predicted novel non-coding RNAs: a miRNA, a snoRNA-derived miRNA, a processed tRNA and a new uncharacterized sncRNA. SeRPeNT facilitates fast and accurate discovery and characterization of sncRNAs at an unprecedented scale. SeRPeNT code is available under the MIT license at https://github.com/comprna/SeRPeNT.