I realize the question states "NFL" but for me it depends on the situation and the sport...and the magnitude of the game.
Last year's Kellen Winslow TD against the Lions that was called incomplete...little miffed at the time, however, when that one bad call became the very thing that kept us out of the playoffs, yeah, I'm still a bit pissed off at that.
England's 2nd goal against Germany in the World Cup, the one that crossed the line, the one that was played as if it hadn't crossed the line, the one that the official stated never crossed the line...I'll hold on to that grudge for a while.