It really bothers me when you ask a question about the best band "EVER" and all you can get for answers are names of bands that didn't exist three years ago. That leads me to conclude that no one is paying attention to the wording of the question.
That rant aside, I would nominate, in chronological order:
ROY ACUFF'S SMOKY MOUNTAIN BOYS. Formed in the mid-30s as the "Crazy Tennesseans," Acuff changed the name of the band because he felt it was derogatory to his home state. With Rachel Veach on banjo and "Bashful Brother Oswald" Kirby on Dobro and harmony, Acuff's band provided the backdrop for the music of the man who became so successful that Japanese kamakazi pilots shouted his name as they attacked Americans during World War II.
BILL MONROE & THE BLUE GRASS BOYS. The "classic" Blue Grass Boys line-up featured Lester Flatt and Earl Scruggs, but other former Blue Grass Boys also included Dave "Stringbean" Akeman, Mac Wiseman, Jimmy Martin, Chubby Wise, Howdy Forrester, Don Reno, and "Ranger Doug" Green.
THE MADDOX BROTHERS AND ROSE. The Maddox Brothers were often described as "ten years ahead of their time" ("TWENTY!" Fred Maddox joked late in life). Their innovations are numerous; their music was carefree; and their family unit ensemble (especially "Friendly Henry the working girls' friend" on mandolin) was unmatched.
HANK WILLIAMS' DRIFTING COWBOYS. The band whose sound has defined country music to many thanks to the legacy of Hank Williams also backed Ray Price as a unit; and, as individuals, recorded countless other country legends.
PORTER WAGONER'S WAGON MASTERS. This band became one of the best-known band thanks to the long-standing television show Wagoner hosted. In addition to the visual antics of Mack Magaha (on fiddle) and the unique sounds of Buck Trent's electric banjo, the members of the band provided some of the best harmony heard on country records in the 60s.
RICKY SKAGGS' KENTUCKY THUNDER. Before he switched back to bluegrass, Skaggs put together an amazing ensemble of pickers who turned out country music at its finest, and have successfully transitioned to bluegrass.
HONORABLE MENTIONS:
Hank Thompson's Brazos Valley Boys
George Strait's Ace in the Hole Band
Jim Reeves' Blue Boys
Riders in the Sky