2013: Robert Covington over Livio Jean-Charles with the 28th pick
The 2013 NBA Draft ranks as one of the worst drafts of the last 10 years, so it's hard to blame the Spurs for not finding a keeper when most other teams didn't either. With the 28th pick, they selected Livio Jean-Charles, a then-athletic 19-year-old 6'9 forward with a massive arm span.
He made for an intriguing prospect who could have eventually played alongside players such as Danny Green and Kawhi Leonard and helped an already terrific defense get even better. Unfortunately, he tore his ACL only a few days after he was drafted.
That stunted his development, and he never improved enough to make the Spurs. That was bad luck on both his and the team's part, but there weren't many players taken behind him that had the Spurs kicking themselves. In fact, the best player after Jean-Charles went undrafted.
Robert Covington was signed by the Houston Rockets and quickly carved out an NBA role as a three-and-d player. 10 seasons later, Covington is still playing in the NBA, and had the Spurs taken him, they would have gotten one of the better wing defenders of the 2010s.