This past week Bill Simmons described the Phoenix Suns of the past few years as a "critically acclaimed" team - teams that didn't win a championship but are remembered fondly outside of their own fan base for their particular style of play or other achievements.
Some teams we'd put in that category:
1998 Minnesota Vikings
This team rode one of the most explosive offenses ever - featuring Randy Moss as a rookie and a rejuvenated Randall Cunningham - to a 15-1 record and 556 points scored. An overtime loss to Atlanta in a great NFC title game prevented a dream Super Bowl matchup between them and the best Broncos team of the Terrell Davis era.
2000-03 Oakland A's
The original Moneyball organization probably had more of an influence on how baseball teams are run than any other in recent memory; they made the playoffs on a shoestring budget four years in a row but never got past the first round.
1987-93 Houston Oilers
Their run-and-shoot offense led by Hall of Fame QB Warren Moon and receivers Haywood Jeffries, Webster Slaughter, Curtis Duncan & Ernest Givens was one of the most fun units to watch in their day. While they made the playoffs seven years in a row in this period, they never made it to the AFC title game and are best known for being on the wrong end of the greatest comeback NFL history and Joe Montana's last signature playoff win.
1994 Montreal Expos
Had the best record in baseball when the strike hit, and the franchise never recovered. Their lineup featured an outfield of Larry Walker, Marquis Grissom and Moises Alou; their rotation included Pedro Martinez, Jeff Fassero (2.99 ERA that year), Ken Hill, and Kirk Reuter. Future World Series MVP John Wetteland and future 40+ saves guy Jeff Shaw in the bullpen.
1995 and 2001 Seattle Mariners
The 1995 team was 12.5 games behind the Angels in mid-August, took the division in a one-game playoff, and won a dramatic Division Series after falling behind 2 games to the Yankees, before losing to Cleveland in the ACLS.
The 2001 team won 116 games and had four All-Star game starters (Ichiro, John Olereud, Edgar Martinez, and Bret Boone). They lost the ALCS in five games to a Yankees team that one 21 fewer games than they did.