He's never that blatant with it, but read the "U2 By U2" book; his arrogance just leaps off the pages at times. Off the top of my head, I remember his comment how he thought Zooropa was a work of genius at the time. And of course his famous comment after the release of All That You Can't Leave Behind about them reapplying for the title of best band in the world just reeks of arrogance.
But, don't get me wrong, Bono's arrogance is a large part of why he is such a great entertainer on stage; he has no fear for doing whatever it takes to make a show great, and that takes a little bit of fearless arrogance.
Little late to the party on this, but I wanted to chime in on this thought in particular. I have "U2 By U2" and I'm familiar with the comment about "best band in the world", so I know where you're coming from, but I take it differently. I don't take it like he KNOWS that, I take it in the sense of "I need to be better". You can say a lot about U2 both good and bad, but you CANNOT say they do things halfway, and you CANNOT say they phone it in. So if that's Bono's way of saying "we're giving it everything we have!" then it's hard to knock. With the new album, supposedly they had an entire album ready to go, and it didn't seem right, so they went back and came up with TWO MORE albums, one of which was released as "Songs of Innocence".
I don't know; I kind of wish more bands pushed the envelope like they do. And for all the comments about Bono, that little fucker can still sing live. You watch him walk out on the runway, with just Edge strumming an acoustic guitar, and you listen to EVERY FUCKING WORD he sings. I think it's a really weak argument to say they aren't one of the three best bands in the world right now (Springsteen is another, and I'll leave the third for the discussion).