Required? No. Preferred? Usually, yes. That said, the degree need not be related to programming or any computer-related discipline. The virtues of the degree irrespective of the field of study are:
Additionally, for young people on the traditional, uninterrupted primary-secondary-college education track, the additional years of physical and emotional maturation are likely desirable.
I've known GOOD analysts, programmers, and engineers from bachelors programs unrelated to IT. My own undergraduate program was in Psych and Math (however, since I contend that programming and data-abstraction are exercises in Applied Boolean Algebra, maybe I shouldn't claim NOT to have an IT/CS degree). Critical thinking, conceptualization, imagination, ethical flexibility, personal responsibility, and confidence are all aspects frequently enhanced by the challenges of completing a degree. The college degree route more reliably and safely leads to the development of the full raft of highly desirable skills and traits than more haphazard paths.
Programming is one of those careers where your roadside, begging sign would read, "Will Think for Food." College does not make people smarter, but, more frequently than not, college will enhance the capacity to think effectively.
Finally, college or not - hire smart, emotionally stable people. Working with stupid or crazy programmers destroys the morale of the smart, stable ones. College offers little filtering of stupid or crazy.