In regards to popular music, there hasn't really been anything commendable. I mean, the sixties had The Beatles and Hendrix, the seventies had Led Zeppelin and AC/DC, the eighties had Guns N' Roses and U2, the nineties had Pearl Jam and Nirvana, the noughties had.... Fall Out Boy and Good Charlotte. You notice the massive drop in talent?
Mind you, the above is all in popular music. Although it may seem like nothing's came out, you just have to look further than what's on the radio, the eighties had the no-wave scene and grunge, the nineties had grunge and indie. The 2000's have been amazing for music. Of course they won't be remembered for much by the majority of people, but if you listen to more than Green Day and Fall Out Boy then you've got a massive spectrum to choose from.
To avoid looking like somebody who wants to shove their music in people's faces, I'll only name a few artists, but if you like any of this music then PM/VM me and we'll share bands or something.
There's the garage-rock revival, bands like The Strokes and The Vines which were prominent in the noughties. There's also been lots of math rock and post rock bands ie. LITE and Explosions In The Sky - even though the genre's been around for a while bands like these take it further. There's been a massive amount of indie rock artists like I Heart Hiroshima and Broken Social Scene. Blues rock like The Black Keys and The White Stripes. Bands that don't fit genres like TV On The Radio and Hella. Electro music, like Crystal Castles and to a lesser extent (as in more rock than electro) Metric. More laid back acoustic music like Jack Johnson and Lisa Mitchell.
Basically, anybody who says that the 00s haven't had their fair share of great musicians is either terribly blind OR just has a different music taste to me. Oh and also, don't pay attention to the genres I mentioned much, it was a large generalisation. Please don't like jump up and down yelling "Broken Social Scene isn't indie!" etc.
What's also good is that the noughties have had so much music to choose from. As in compared to what's out there I know hardly any bands at all. So even if music gradually gets worse in the future, we've still got years and years of more listening behind us now.