As a Dolphins fan, this is tough one, but it's essential to the list.
Brees injured his shoulder at the end of the 2005 NFL season. He wasn't going back to the Chargers, who were handing over the car keys to Phillip Rivers.
Brees had two teams realistically competing for his services. One was the Miami Dolphins, who were a team on the rise and were even picked by Sports Illustrated to go to the Super Bowl the following year.
The other team was the New Orleans Saints, a franchise that finished 2005 with one of the worst records in the league, and who's home stadium yielded comparisons to a level of hell after their city was hit with arguably the worst natural disaster in American history.
You would think that anyone in their right mind would go with Miami, unless the management was incompetent and the coach was more concerned with applying for college coaching jobs than doing the current one he held. Luckily, for Saints fans, that was exactly what was going on in Miami.
Brees chose the Saints over the Dolphins. In the four year stretch since the signing, Miami hasn't won a playoff game, but they have produced a 1-15 season.
Meanwhile, the Saints have four times as many playoff games in Brees' tenure than they had as an entire franchise prior to the signing. I watched Brees hold the Lombardi trophy and Super Bowl MVP trophy this past February and died a little inside.