The Excitement Index (explained here) lets us measure how riveting a game was. Here are the average EIs for the division round games by year since 2001.
This year ranks second only to 2009, when NO beat ARI 45 to 14, IND beat BAL 20-3, MIN beat DAL 34-3, and NYJ beat SD 17-14. The NYJ-SD game was was decent 4.2 on the EI scale, but the other games were dogs.
This year, the most exciting game was SF-CAR with an EI of 3.1. For comparison, Last year's BAL-DEN heart-attackathon was an 8.5, which moved the Win Probability needle more than 3 of the 4 games of 2013 combined.
2006 leads the pack as the season with the most exciting division round. That year IND beat BAL 15-6 in what was the snoozer of the weekend (3.8 EI). NO squeaked by PHI 27-24 (5.3 EI). CHI edged SEA by the same score (7.5) EI. And NE beat SD 24-21 (6.7 EI).