Warren Moon is quite possibly the one quarterback on this list who overcame the most on his way to greatness. He was not recruited by any major college to play quarterback, so he went the junior college route, where he impressed enough to get an offer from Washington. Despite a strong senior year, he went undrafted in 1978, so he ended up going to play in the CFL.
During his first 5 seasons in Canada, Moon and the Edmonton Eskimos won 5 consecutive championships, a feat that is still unmatched, and he set league records in passing yardage in both 1982 and 1983. After setting numerous records in Canada, he finally received a lot of interest from the NFL, and he finally signed on with the Houston Oilers.
His first 3 years in the NFL did not go quite as planned. He was starting every game for Houston, but he threw more picks than touchdowns in each of those seasons. He finally pulled it together in 1987, when he led Houston to their first playoff berth since 1980 and even won a playoff game, something he did not do much over the rest of his career.
He continued to improve steadily over the next few years, peaking in 1990, when he led the league with 4689 yards and 33 touchdowns, while throwing only 13 interceptions. He wasn't able to win in the playoffs, but he came back strong again in 1991, again topping the league in passing yards. That season he won a playoff game for the third and last time in his career, meaning that he never even saw a conference championship game.
He remained a starter in the league for another 7 years, but could never translate the regular season success to the playoffs. He had an incredibly long career, playing 17 seasons in the NFL after 6 seasons in Canada, and he started the majority of his team's games in each of his first 15 seasons. When he retired, he was in the top 5 all-time in completions, attempts, yardage, and touchdowns. He was also the first black quarterback elected to the Hall of Fame, and at the same time became the first undrafted quarterback to be enshrined. He may not have the playoff success of many of the QB's on this list, but very few can match the sheer volume he put up over the course of his career, which is why he is in this spot.