I'm glad the Green Bay Packers have generally avoided veteran free agents each offseason under GM Ted Thompson. My first thought is that if their former team is willing to let them go, then they are probably right since they know more about that player than any other team could ever learn.
The obvious, glaring exception over the past few years was the signing of CB Charles Woodson. He was widely regarded as done, and signed with the Packers because no one else was interested. That's one exception, and the annual free agent carousel is littered mistakes. And I'm glad they avoid it.
A couple years ago, the Vikings had a free agent decision to make with C Matt Birk. It was a tough decision, but his high price tag and declining production made them look elsewhere. Ravens fans are probably glad they did. In 2010, his play was arguably just as good as the player widely regarded as the best center in the NFL: Jets C Nick Mangold. From Pro Football Focus:
The point of all this? Matt Birk is a six-time Pro-Bowler. 2010 should have made it seven. Whether you think he can keep up with the dominant play of Mangold or not (and there’s a very valid argument to be made that if Mangold is healthy for all of next season he will avoid much of the negatives of 2010), Matt Birk is still capable of being one of the league’s best centers, and all too many people seem to have forgotten that.
While I wasn't sure how well Birk had played over his last couple seasons with the Vikings, the center position in general is not an easy position to evaluate, it seemed like the Vikings were making the right decision at the time. But it's probably a free agent decision they'd like to take back.