1995-Kevin Garnett (5th pick Minnesota Timberwolves)
Simply put, Kevin Garnett put the Timberwolves franchise on the map. He was drafted as a high schooler and quickly became the franchise centerpiece that every team thinks about when they draft these young guys. Garnett was never able to win a championship in Minnesota, but they enjoyed more success during his tenure than they ever have before or since. The franchise has only made the playoffs eight times and all eight of those happened in a row when Garnett was leading the team. Garnett was such a relentless player that played with so much passion and you wanted to see him win. Unfortunately, the team did not do well to build a team around him and the best they could do was get to the Conference Finals in 2004, the same year that Garnett won the MVP. He was everything to the Timberwolves and I would argue he is still beloved in Minnesota.
1996-Allen Iverson (1st pick Philadelphia 76ers)
I am not a huge fan of Iverson, but you cannot deny what he meant to the city of Philadelphia during his time as a member of the 76ers. They completely embraced the 6'0 guard with the heart of a lion that was relentless in his game and played the game with so much passion and energy. Say what you will about his lack of efficiency, but Iverson was part of some pretty successful teams in the early 2000's leading the Sixers to the Finals in 2001, where he somehow stole a game from one of the most dominant playoff teams ever (2001 Lakers). He won the MVP award in that season and was consistently representing the 76ers on All-NBA teams and in All-Star games. Iverson was beloved in Philly and he was a heck of draft pick.
1997-Tim Duncan (1st pick San Antonio Spurs)
This was the easiest draft to do because it is unquestionably Tim Duncan, who might be the greatest draft pick of all time. The longevity, the success, and the class are unparalleled by anyone in the history of the NBA. Tim Duncan won 5 championships with the Spurs, along with 19 seasons straight of making the playoffs and winning over 60 games 5 times. Tim Duncan made it to the 2nd round of the playoffs and beyond 15 times. No player had such a huge impact on their franchise for so long. Tim Duncan won so many awards and was named to so many All-NBA teams that it is hard to imagine a player doing more for one team, the team that drafted him. He won league MVP 3 times and is without a doubt the greatest Spur and one of the 10 greatest players to ever play the game.
1998-Paul Pierce (10th pick Boston Celtics)
Pierce started out his career as the 10th pick in an NBA Draft where many felt he should have been taken in the top 3 or 4, but he slipped to the Celtics and little did the know that he would mean so much to the franchise. Pierce was drafted to a Boston team that was not very good. He became a great player in the NBA quickly and teaming with Antoine Walker, the Celtics made it to the Conference Finals in 2002 and would make the playoffs three years in a row after that. Pierce looked to be a good player stuck on a bad team and for two years the Celtics were bad, but they were able to add Kevin Garnett and Ray Allen in the summer of 2007 and Pierce was able to bring the Celtics back to prominence with a title in 08 along with a Finals MVP Award. Pierce would help the Celtics get to the Finals again in 2010, but they could not win another championship. Pierce would be traded to other teams, but he was always thought of as a Celtic and he is one of the best to ever play in the league.
1999-Manu Ginobili (57th pick San Antonio Spurs)
Ginobili is the first 2nd round choice mentioned on the list and he might be the only one. Ginobili joined the San Antonio Spurs three years after they drafted him and his impact was immediate helping them win a championship in his rookie season. He would win 4 championships in total with the Spurs and would be a perfect wing to play alongside Tim Duncan. Ginobili is such a vital part of the Spurs and what they did as an organization and he continues to keep coming back for more having just signed a two year extension to continue playing for the team that drafted him. While he may be slowing down, the people of San Antonio don't mind seeing Manu on the court.