As of 2014, there has only been one NFL team to finish a season 0-16. That team was the 2008 Detroit Lions. Before the Lions, the last NFL team without a win was the 1976 Tampa Bay Buccaneers, although that was before the schedule expanded to 16 games.
Over the course of the 2008 season, the Detroit Lions scored 268 points and allowed 517 points. Six of the team's losses were by less than 10 points, including a two-point loss to the Minnesota Vikings in Week 6, which was the closest it came to a win all season. The Lions had won all four of their games during the preseason.