I throw out the challenge. The Cleveland Browns are the standard for futility.
The Buffalo Bills have not made the playoffs since 1999. They have not had a season at or above 8-8 since 2004.
Since the league expanded to 32 teams in 2002, 31 of them have made the playoffs at least once. The lone exception? The Bills.
There are, to be sure, a few teams that come close. The Browns and Oakland Raiders certainly rank right up there. But in terms of long-term futility in the modern era, the Bills are at the top. At least the Browns have Johnny Football to look forward to... eventually. The Bills pinned their hopes on a quarterback from one of the weakest draft classes in modern memory.
And yet, with all that baggage, the Bills had at least two bids over a billion dollars for the team, one from Toronto (Jon Bon Jovi and a couple Canadian billionaires who were not so secretly trying to relocate the team to Toronto) and another from the locally born and raised wife of a multibillionaire who made his fortune in Pennsylvania gas fracking and cashed out a couple years back. Kim Pegula won. Had the NFL and Ralph Wilson's estate not been so restrictive about keeping the team in Buffalo, LA interests would have bid the price up even higher and might very well have won.