Over the last decade, structural biologists have unravelled many proteins that appear natively disordered. Common assumptions are that many of these proteins adopt structure through binding and that the structural flexibility enables them to adopt different functions. Here, we investigated regions of more than 70 sequence-consecutive residues that have no regular secondary structure (NORS). Analysing 31 entirely sequenced organisms, we predicted five times as many proteins with NORS regions (loopy proteins) in eukaryotes (20%) than in prokaryotes and archaeas (4%). Thousands of these NORS regions were over 150 residues long. The amino acid composition of NORS regions differed from that of loops in PDB. Although NORS proteins had significantly more residues in low-complexity regions than other proteins, simple cut-off thresholds for sequence bias missed most NORS regions. On average, NORS regions were evolutionarily at least as conserved as their flanking regions. Furthermore, yeast proteins with NORS regions had more protein-protein interaction partners than other proteins. Regulatory and transcription-related functions were over-represented in loopy proteins, biosynthesis and energy metabolism were under-represented. Overall, our analysis confirmed that proteins with non-regular structures appear to play important functional roles, and they may adopt as yet unknown types of protein structures.