The first, and only, case of a tiebreaker deciding a playoff spot prior to the AFL-NFL merger was a notable one. In 1967, the Baltimore Colts entered the final week of the regular season at 11-0-2, trying to become the first team to go undefeated since the 1929 Green Bay Packers. However, they had to travel to Los Angeles to face the 10-1-2 Rams, their Coastal Division rival. The Rams won that game, and the tiebreaker, on net points scored in the two head to head matchups, and advanced to the playoffs. The Colts, despite tying for best record in the league, stayed home.
In Divisional tiebreakers, five three way ties have been used. Four were determined affirmatively by head to head record (that is, one team had either a 3-1 or 4-0 record combined against the other two), and one, the AFC East in 2002, was determined in the negative by kicking out Miami based on division record (2-4 versus 4-2 for both the Jets and Patriots).
Virtually all the divisional tiebreakers have been decided by either head to head, division record, or conference record, with head to head being the most common.
I hope this helps :)