Rivalries are a tricky thing to figure out. They can pop up unexpectedly, or be entrenched in team history. They can be focused more around a group of players, or they could be so deep that the franchises themselves seem to breed dislike for one another amongst fans and players alike.
In the decade from 2000-2010, few rivalries were more noteworthy or exciting than the Colts/Patriots rivalry. Peyton Manning vs Tom Brady was always a good prime time matchup, and over the years the teams took turns disrupting one another in some epic showdowns.