Genetically diverse influenza A viruses (IAVs) circulate in wild aquatic birds. From this reservoir, IAVs sporadically cause outbreaks, epidemics, and pandemics in wild and domestic avians, wild land and sea mammals, horses, canines, felines, swine, humans, and other species. One molecular trait shown to modulate IAV host range is the stability of the hemagglutinin (HA) surface glycoprotein. The HA protein is the major antigen and during virus entry, this trimeric envelope glycoprotein binds sialic acid-containing receptors before being triggered by endosomal low pH to undergo irreversible structural changes that cause membrane fusion. The HA proteins from different IAV isolates can vary in the pH at which HA protein structural changes are triggered, the protein causes membrane fusion, or outside the cell the virion becomes inactivated. HA activation pH values generally range from pH 4.8 to 6.2. Human-adapted HA proteins tend to have relatively stable HA proteins activated at pH 5.5 or below. Here, studies are reviewed that report HA stability values and investigate the biological impact of variations in HA stability on replication, pathogenicity, and transmissibility in experimental animal models. Overall, a stabilized HA protein appears to be necessary for human pandemic potential and should be considered when assessing human pandemic risk.