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It's not clear if you're asking if anyone died while an active player in the NFL, or if anyone has died on the field during a NFL game. Active players have died during off season and a few have died as a result of an injury during a game, but I can find only one that actually died on the field during a game.

From ESPN http://espn.go.com/page2/s/list/football/shocking/moments.html
Detroit Lions receiver Chuck Hughes dies of heart attack during game (Oct. 24, 1971)
The Lions trailed the Bears 28-23 late in the fourth quarter, and had the ball. With the Lions running a two-minute drill, wide receiver Chuck Hughes came into the game, and went deep over the middle on a play that ended with an incomplete pass intended for another receiver. As he headed back to the huddle, he collapsed. Bears middle linebacker Dick Butkus got to him first and alerted the Lions bench. Team doctor Richard Thompson came onto the field and tried to resuscitate Hughes, unsuccessfully. The game was finished in silence.

Also, there have been two players die during training camp. Most recently, Korey Stringer in 2001 and J.V. Cain in 1979. According to USA Today http://www.usatoday.com/sports/football/nfl/redskins/2007-11-27-taylor-death_N.htm there have been 7 NFL players die from 2001 to 2007, but none have been on the field.