The classic case, for me, is Mark Prior. He was one of the most hyped pitching prospects in history (with supposedly a "perfect" delivery, even though his inverted W was destroying his shoulder and arm), and when the Cubs called him up, it seemed like a whole new era was coming to Wrigley Field: Kerry Wood was healthy again, Aramis Ramirez had been stolen from Pittsburgh (for Jose Hernandez

), Juan Cruz was throwing fireballs, Corey Patterson hadn't been exposed as one-dimensional yet, and here comes Prior, just making batters look like absolute fools, left and right. If he wasn't blowing someone away with his fastball, he was getting them to drill themselves into the dirt trying to hit his utterly filthy curve ball. Dude looked like he had everything and was going to be The Guy in the Cubs' rotation for years to come.
... And then his arm fell off. Overuse in the minors and especially in 2003 in the majors caught up with him and multiple surgeries followed. In 2006, just a few years after his 2002 debut, Prior threw his last pitch in Major League Baseball. He's currently the Dodgers' pitching coach, so he got himself a ring, which is badass, but, still ... what a career he could have had.
Some other guys that come to mind are obviously Doc Gooden and Darryl Strawberry; both of them could and should have been all-time legends and had every opportunity to straighten themselves out, but their love of nose candy was just too strong, leaving them as mere footnotes in history as opposed to the deities of a minor pantheon they could have been.
Loath as I am to express sympathy for a Cardinal, Rick Ankiel is another What If? case for the ages. Absolutely dominant stuff and command, and then out of the blue he caught Steve Blass disease in the 2000 playoffs. It was like watching someone get a Chuck Knoblauch case of the yips in real time. Yeah, he was able to string together a few mediocre seasons as an outfielder (although he never improved beyond "newborn giraffe" when it came to his route-taking abilities), but if he hadn't had something snap in his brain, he could have had a special career.
Speaking of snapping, that just reminded me of Tampa Bay pitcher Tony Saunders. Regarded as a surefire thing despite already having had Tommy John surgery at age 20, the Rays were excited enough about him to make him their first expansion draft pick. And then in the middle of a summer game, Saunders delivered a pitch and then unleashed one of the most unholy screams I have ever heard. With one throw, he had broken his arm and torn pretty much every ligament in it.
Saunders was a gamer, though. He worked his ass off to rehab his arm, and made it all the way to a high-A rehab assignment to really get back into pitching condition.
And then he suffered the exact same injury in the exact same place: Shattered arm, shredded ligaments. He announced his retirement through his agent that very night. I remember watching SportsCenter that night when his arm blew up a second time and all I could think was, "No fucking way."