It's not uncommon to see a player flop in the NBA (remember Chris Paul?), but it would seem that the technique is also quite common in the NFL. 

Brian Urlacher, the recently retired former Chicago Bears linebacker, admitted that the team had a "dive guy" in place to slow down high-intensity offenses by faking an injury. They certainly aren't the only team to do this, and they won't be the last.

Urlacher added that his team wasn't coached faking injuries, but it was practiced as part of their game. The coach would even make a "dive" gesture on the sideline to signal when the designated player would, presumably, collapse on the field writhing in agony.

In 2011 the New York Giants were caught flopping, which led to the NFL's issuing a warning to all teams about faking injuries.