For a small market team, the Jazz have had a lot of big names come through the rankings. Guys like Karl Malone, John Stockton, and then you had some awesome front courts with Al Jefferson. A lot of guys were able to stay healthy for most of their time for the Jazz, and some were not. Back in 2002 you had Jarron Collins tear both his ACL and MCL in his knee, and he missed the season. Keon Clark a few months later had to have surgery to remove bone spurs, and missed two months. More bad luck game with Ben Handlogten and Matt Harping had to miss the 2004 season both with knee injuries.
Remember Andrei Kirilenko? He was a Russian draft pick for the Jazz, who fizzled out in the middle of his career. He missed most of the 2005 season with a broken wrist. Kyle Korver played in Utah, although it really is not his most notable place. In 2009 he had to miss time due to knee surgery so he could remove bone spurs. In 2010, Mehmet Okur missed the rest of the season and some of 2011 with a torn left Achilles tendon. Mo Williams missed part of the 2012-2013 season with a thumb injury, that later required surgery. Playing through it might have made this problem worse, and he missed a lot of the second half because of it.
Later in the 2013 season, Enes Kanter had to have surgery to repair a dislocated shoulder. This came right before Marvin Williams had surgery on his Achilles tendon. This was a brutal stretch for the Jazz, missing a few key guys in the front court. Brandon Rush had to have surgery on a torn ACL, and Rush was another productive college player who suffered many injuries in the NBA. Rush never got it going with any team. While Alec Burks is just a role player for the Jazz, they missed his scoring off the bench in 2014 when he missed half the season with a shoulder injury.
The young Australian point guard, Dante Exum tore his ACL back in 2015 at the beginning of the season. Exum has yet to establish himself in the NBA, and this injury was a big reason why. It will be tough for him to get going, but early on in 2018 he looks to have made a jump. Burks suffered a fractured fibula in 2016, causing him to miss the rest of the season. Since then things have been somewhat calm. Exum did have to have surgery at the beginning of 2017, but he was not featured in the Jazz rotation much anyway.