The NFL does not require a degree, but does have an age requirement which occasionally comes up as a hot debate point: "The NFL Eligibility Requirements NFL rule requires a player to either be out of high school for three years or have finished three college football seasons before joining the league. (Lupica, M. 2004) The NFL is the only major professional sport that prohibits the drafting of players who have not completed three college seasons or who are not three years removed from high school graduation (Gehring, 2004; Nieporent 2004). The NFL claims that this rule is in the athlete's best interest. The NFL argues that this rule protects player’s physical safety. However, the NFL and the NCAA benefit by capitalizing on amateur athletes."

http://www.thesportjournal.org/article/age-requirement-profe...

To be drafted by the NBA you have to be "at least one year out of high school".

http://en.wikipedia.org/wiki/Eligibility_for_the_NBA_Draft

The degree is not required, but this forces most into at least one year of indentured service to a college. You can sit out, but how will you be evaluated for the draft?