In the early days of the NFL, it was not uncommon for a team's quarterback to pull double duty as a punter or kicker, but this practice was almost completely phased out by the late 1960's, when player specialization really took hold. The only notable exception in the past 50 years was Danny White, Dallas' quarterback for much of the 1980's, who also handled the team's punting for 8 seasons.
White set 7 NCAA passing records during his career at Arizona State, but was disappointed to be drafted by the Dallas Cowboys, who had a star quarterback in the prime of his career by the name of Roger Staubach. Dallas wanted to bring him in as a punter, but he felt he belonged at QB, so he joined the USFL for a couple years before the league folded and he decided to take Dallas' offer to play punter and backup quarterback. In that role he was a member of the Super Bowl XII champions, and even got the chance to play quarterback for a series in the fourth quarter. He spent 4 years backing up the legend in Dallas before finally getting his chance at the helm in 1980.
None of the above helped White make this list, because punting statistics were not counted toward greatness at the QB position, and he wasn't a major contributor to the championship, but when he stepped in to replace Staubach, he was almost immediately one of the top quarterbacks in the league. During each of his first three season as the starter, Dallas advanced to the NFC championship game, but fell short each time in its bid to reach the Super Bowl. For this reason, plus the fact that he was being compared to his predecessor, White has never been fully appreciated by football fans.
His best overall season came in 1982, which was shortened to 9 games due to a strike, when he finished with 2079 yards and 16 touchdowns, both #4 in the league during the short season. He again finished among the top 5 in both categories the following season, with 3980 yards and 29 touchdowns for a full season, but his team lost in the wild card round and White lost his starting job to open the next season.
When Gary Hogeboom, his former backup, began struggling midway through the 1984 season, White was reinstated as the starter and nearly got his team back to the playoffs, missing out due to a tiebreaker. The following season he led them back to the playoffs, but the season ended in disappointment again with another first round playoff loss.
In 1986, the Cowboys were in first place midway through the season and White was the top-rated passer in the league when he suffered the only major injury of his career, a broken throwing wrist, which ended his season and, eventually, his playing career, as he was never able to return to his previous form.
In the five seasons in which he was the unquestioned starter, he led Dallas to the playoffs five times, three times advancing to the conference championship game. Although he never led his team to the Super Bowl, he led one of the NFL's best offenses for most of a decade, which is why he is included among the top 50 quarterbacks of all time.