Hogwarts co-founder Salazar Slytherin (who left because he opposed the education of non-pureblooded wizards) was reportedly a Parselmouth as well. The Chamber of Secrets was supposed to be openable only by an heir of Slytherin, and, as it turns out, the Parselmouth ability figured in this.

When Potter was found to speak Parseltongue, rumors spread that he might be an heir of Slytherin, but this turned out to be false; in fact, he may actually be a descendant of Godric Gryffindor, the founder who opposed Slytherin and supported a less discriminatory admissions policy.

The origins of Potter's Parseltongue ability aren't definitively established, but it's surmised in one of the books that he might have received it along with his lightning-shaped scar when Lord Voldemort tried unsuccessfully to kill him as an infant, accidentally transferring some of his powers.