Can a NFL player be traded during the season?

Yes, up until the trade deadline which is the Tuesday after the sixth week of the season. http://en.wikipedia.org/wiki/Trade_deadline#NFL However, the NFL is a league that is not geared towards the trading of veteran players as a primary means of improving one's team. The nature of NFL contracts and salary cap, as well as the physical nature of the game (which thus raises the injury risk on all players), and the complex nature of NFL playbooks and teamwork relative to other sports makes it rare to trade a player during the offseason and during preseason, and almost unheard of once the season has begun.