It's impossible to talk about mid-to-late round quarterbacks who have gone on to have successful NFL careers without talking about New England's Tom Brady, who has three Super Bowl rings despite being drafted in the sixth round back in 2000.
The truth is it's easy to see why Brady lasted so long when you evaluate his collegiate career at Michigan. After finally winning the starting job as a junior in 1998 and being named a captain before the start of the 1999 season, Brady split time with Drew Henson during his senior year. Additionally, he didn't show elite arm strength on film and teams were concerned about the ability of the 205-pounder to take the kind of pounding quarterbacks endure at the NFL level. In fact, New England scouted him because it was in the market for a backup to Drew Bledsoe, not a potential starter, and didn't realize it had one of the great steals in NFL draft history until two years later.
Brady spent his rookie season learning the Patriots' playbook and, just as importantly, adding weight to his frame. So even though few knew anything about him when he replaced the injured Bledsoe in Week 2 of the 2001 season, Brady was ready to step in and played with rare confidence for a young quarterback. It's also worth pointing out that Brady could have geared down after leading New England to its first-ever Super Bowl win that season and being named the game's MVP, but he didn't. Instead, he continued to get stronger and greatly improved his ability to put zip on downfield passes while improving his ability to read coverage and get the ball to the open man.