Max Scherzer, 2003, 2014, and 2021
Yup. The Cardinals passed on Max Scherzer three times, the first instance being when they drafted him.
Scherzer was a local prospect who was coming out of high school, but the Cardinals did not offer him enough money as a 43rd-round pick to make it worth skipping college. He was later drafted 11th overall in the 2006 draft by the Diamondbacks.
After an incredible beginning to his career and winning his first career Cy Young in 2013, Scherzer was a free agent in the 2014 offseason, but the Cardinals did not seriously bid on him and he went to the Nationals on a seven-year, $210 million deal. Scherzer won two Cy Youngs during that contract, finished second one, and third twice while going 99-47 with a 2.75 ERA over the course of it.
Then after the 2021 offseason, Scherzer was once again a free agent, looking for a short-term deal with a record AAV. The Mets decided to grant him his wish, signing him to a three-year, $130 million deal. While this season has not gone well for Scherzer, he did go 11-5 with a 2.29 ERA in 145.1 innings last year.
Not signing him in 2021 is slightly defensible, but passing on him in 2003 and 2014 were huge mistakes. They did not sign their local high school product which could have been a huge asset in the early 2010s (he won Cy Young in 2013, the year they lost the World Series). And then they said no thanks in 2014 when the very next offseason they pursued Price with a similar kind of deal.