For decades, researchers have studied the rapid evolution of influenza A viruses for vaccine design and as a useful model system for the study of host/parasite evolution. By performing an exhaustive analysis of hemagglutinin protein (HA) sequences from 49 lineages independently evolving in birds, swine, canines, equines, and humans over the last century, our work uncovers surprising features of HA evolution. In particular, the canine H3 stalk, unlike human H3 and H1 stalk domains, is not evolving slowly, suggesting that evolution in the stalk domain is not universally constrained across all host species. Therefore, a broader multi-host perspective on HA evolution may be useful during the evaluation and design of stalk-targeted vaccine candidates.