1. Boomer Esiason
I debated putting Burrow here but ultimately, the top spot is going to Boomer Esiason. The Bengals spent a second-round pick on Esiason in the 1984 NFL Draft, making him the first quarterback taken in that year's draft.
Esiason joined the Bengals when Ken Anderson was still with the team but did receive some playing time. He started four games as a rookie and won three of them. He took over as the full-time starting signal-caller in the 1985 season and by 1988 was one of the best quarterbacks in the league.
During that 1988 season, Esiason threw for 3,572 yards, 28 touchdowns, and 14 interceptions while rushing for 248 yards and one touchdown with his legs. Esiason's efforts earned him the NFL MVP award in 1988 and the Bengals reached the Super Bowl for just the second time in franchise history.
Esiason was traded to the Jets in 1993 but returned to Cincinnati in 1997, which was the final season of his storied career. He finished his Bengals tenure with 27,149 yards, 187 touchdowns, and 131 interceptions with 1,355 rushing yards and five rushing touchdowns.
While Esiason never won a Super Bowl with the Bengals, he sits at the top of the list because he got the team there and also won an MVP. Burrow is going to win a Super Bowl in the next few years and likely an MVP award too but until he does either of those things, Esiason gets the top spot here.