While I don't expect that this passage would convert any "non-believers" into U2 fans, it nevertheless sums up many of the thoughts I have about my own passion for the band.

" . . . perhaps the most essential truth about U2 and their work. U2 are not important because they sell millions of records, although it is important that they have achieved such success. U2 are a popular music phenomenon not simply because they make phenomenally popular music.
U2 remain the most important, with the exception of REM perhaps the only consistently essential rock 'n' roll band of the past decade, because the music in all its glory, with all its mistakes, with all its yearning, with all its overambition, with all its passion, with all its underachievement, uncertainties, its successes and failures, reminds us all of our own human frailty. It is music made by ordinary men in an extraordinary situation who have rarely forgotten their roots . . ."
Dave Bowler & Bryan Dray, U2 - A Conspiracy of Hope, 1993

Words of glowing praise they may not exactly be, but in reality U2 have got where they are by being ordinary, real, passionate and by maintaining artistic control over their activities, not by being manufactured and packaged in accordance with current trends. I believe that gives many of us hope of achieving great things ourselves.

U2's music is a music of contrasts, from the darkness of Exit and Love Is Blindness to the light of Beautiful Day or Sweetest Thing, from the traditional (Van Diemen's Land, Running To Stand Still) to the contemporary (Elevation), from the wide open spaces (Where The Streets Have No Name) to the claustrophobic (Acrobat), from gospel (I Still Haven't Found What I'm Looking For, Rejoice) to the music of the Devil (The Fly).

While I have great fondness for The Joshua Tree album and am in awe of Achtung Baby, my love for the music of U2 spans their many different eras. My definitive U2 compilation would look something like this
(in an approximate Top 20 order that may vary on any given day):