Conformational variation in catalytic residues can be captured as alternative snapshots in enzyme crystal structures. Addressing the question of whether active site flexibility is an intrinsic and essential property of enzymes for catalysis, we present a comprehensive study on the 3D variation of active sites of 925 enzyme families, using explicit catalytic residue annotations from the Mechanism and Catalytic Site Atlas and structural data from the Protein Data Bank. Through weighted pairwise superposition of the functional atoms of active sites, we captured structural variability at single-residue level and examined the geometrical changes as ligands bind or as mutations occur. We demonstrate that catalytic centres of enzymes can be inherently rigid or flexible to various degrees according to the function they perform, and structural variability most often involves a subset of the catalytic residues, usually those not directly involved in the formation or cleavage of bonds. Moreover, data suggest that 2/3 of active sites are flexible, and in half of those, flexibility is only observed in the side chain. The goal of this work is to characterise our current knowledge of the extent of flexibility at the heart of catalysis and ultimately place our findings in the context of the evolution of catalysis as enzymes evolve new functions and bind different substrates.