No one who Belichick cuts or trades has done better when they went elsewhere.
Not always true.
Terry Glenn - Resurrected his career in Dallas, including two seasons in 2005 and 2006 that rival anything he did with New England (aside from his brilliant rookie season, of course).
Drew Bledsoe - His first season in Buffalo put him back in Pro Bowl form for the first time since 1997. His performance did drop considerably after that, but still.
Adam Vinatieri - Helped the Colts win a Super Bowl, providing a major upgrade from Mike Vanderjagt (the anti-clutch).
Asante Samuel - Two consecutive Pro Bowl appearances with the Eagles (didn't deserve it in 2008 though)
Dave Thomas - More catches and receiving yards in 2009 than his three combined seasons in New England. Also got a ring with New Orleans.
Andre' Davis - Found his niche as a kick returner for the Texans.
Jabar Gaffney - Career-best season statistically with Denver last season.
Kelley Washington - Career-best season statistically with Baltimore last season.
Joey Galloway - Being facetious here, though he does already have more receiving yards this season with Washington than he did with New England last season.
Dan Klecko, Heath Evans, and Randall Gay are some players who, while not necessarily as productive as with the Pats, got rings after leaving New England. But that's bound to happen with the law of averages.
I will concede, though, that the Pats are more often right than wrong when they cut ties with a player, and that was the point of this thread.