1. The Zaza Pachulia incident
While Ray Allen's Game-6 shot in 2013 was certainly a franchise-altering event, the team used that loss as motivation to win the championship the following season. Whereas the Zaza Pachulia incident arguably had more far-reaching ramifications.
During Game 1 of the 2017 Western Conference Finals, San Antonio was up by 21 points over Golden State, with 8 minutes left in the 3rd quarter. Then the Warriors' center, Pachulia, slid his foot out underneath Leonard on a closeout for the second time in the game, that time causing Leonard to injure his foot.
San Antonio ultimately lost the game without Leonard, as well as the series due to his absence. Had Leonard stayed healthy, San Antonio possibly would have beaten Golden State as well as the Cleveland Cavaliers en route to their 6th championship.
That didn’t happen, however. Golden State would go on to win the NBA championship while Leonard would request a trade a year later. Whether intentional or not, Pachulia effectively ended the Spurs' run as a contender. As a result, Leonard's injury was the event that most dramatically altered the direction of the franchise.
It will likely take several seasons for San Antonio to make it back to the playoffs. Fortunately, the Spurs already have a solid young core, as well as virtually all of their draft picks, including the four picks acquired this offseason. Overall, the franchise’s direction may have been altered by these events, but it appears that the team is now moving in the right direction.