The significance of hydrogen bonding and its variability in polymorphic crystal structures is explored using new automated structural analysis methods. The concept of a chemically equivalent hydrogen bond is defined, which may be identified in pairs of structures, revealing those types of bonds that may persist, or not, in moving from one polymorphic form to another. Their frequency and nature are investigated in 882 polymorphic structures from the Cambridge Structural Database. A new method to compare conformations of equivalent molecules is introduced and applied to derive distinct subsets of conformational and packing polymorphs. The roles of chemical functionality and hydrogen-bond geometry in persistent interactions are systematically explored. Detailed structural comparisons reveal a large majority of persistent hydrogen bonds that are energetically crucial to structural stability.