Until now, this honorific has fallen to The Beatles. Their crown is only threatened by arguments made in favor of The Rolling Stones or Led Zeppelin Those have been the only three bands with the artistic, commercial, and musical chops to lay claim to being the greatest rock band of all-time.

The Who, Grateful Dead, Pink Floyd, Eagles, AC/DC, The Clash, The Police, Talking Heads, The Smiths, Deftones, Nirvana, Pearl Jam, and Radiohead are all on the second-tier thanks to at least one glaring weakness (a relative glaring weakness like being short-lived, lacking commercial appeal, inconsistency, etc.). Yet, if we look at U2's resume they not only enter the argument, they win it.

Commercial Success

U2 has sold more than 170 million records.  There's only seven bands that have sold more music then they have.  All of those bands started moving product years before U2 even formed. 

Also, as a band, U2 is fairly young (compared to the other acts we've mentioned).  They've got a lot of good years in front of them to add to their numbers.

Touring Success

The "U2 360 Tour" is the highest grossing concert tour of all-time. Adjusting for inflation, it grossed $784,027,536.  Their "Vertigo Tour" is the sixth highest grossing concert tour of all-time.

This year, they're launching a new tour, and tickets are on sale for "The Joshua Tree Tour 2017." That trek will only add to their touring success.  Quite simply, U2 is the greatest touring band of all-time.

Chart Success

U2 has charted seven number one albums and two number one singles.

Awards

U2 has won 22 Grammy Awards. That's the most Grammy victories for any band. 

They are also members of the Rock and Roll Hall of Fame.  They were inducted in their first year of eligibility.

Longevity

Some bands are disqualified from greatest band of all-time status because they weren't around long enough.  U2 formed in 1976 and released their first album in 1980.  How's that for longevity?

Also, from their first recording onward, the band has kept the same lineup: Bono, The Edge, Adam Clayton, and Larry Mullen, Jr.

Critical Success

U2 doesn't have just one, they have several critically acclaimed albums: Achtung Baby, All That You Can't Leave Behind, How to Dismantle an Atomic Bomb, No Line on the Horizon, The Unforgettable Fire, War, and Zooropa.

Of course, they also have a "Sgt. Peppers" or should we say The Beatles have a "Joshua Tree?"  To be the greatest band of all-time you need to have made the greatest album of all-time.  U2 has made it.  It's Joshua Tree.

The Ear Test

Just listen to U2.  Their sound is big.  Their songs are big.  They are big.

You can't be the greatest band of all-time if you write and record small songs.  U2 writes and records huge anthems. Their songs are important, perhaps the most important songs ever written. 

"Pride (In the Name of Love)," "I Still Haven't Found What I'm Looking For," "Where the Streets Have No Name," "Mysterious Ways," "One," "Beautiful Day," and "City of Blinding Lights" are giant, powerful anthems, that by their sheer size, dwarf other songs.

How can you compare little ditties like "I Want to Hold Your Hand," "Honk Tonk Woman" and "Black Dog," to majestic rock hymns like "The Unforgettable Fire," "All I Want Is You," "Even Better Than the Real Thing" and "Miss Sarajevo."

Conclusion

U2's longevity and success is unparalleled.  Even better, they write and record huge anthems, the kind you'd expect the greatest rock band to perform. 

After looking at U2's resume, only one conclusion can be made.  They are the greatest rock band of all-time.