Was King of the Hill a "Villain of the Week" show?
More than often, you had people with alternative lifestyles presented in a negative light, people who seemed good but had ulterior motives, and those who just were wrong because they don't know better.
The show did have recurring antagonists (Cotton, the social worker at the beginning, and later Thaferton), but they mostly invented characters to be obstacles.
Even family members (Peggy's mother and Boomhauer's brother) come to mind.