I'm not very quick at discovering new bands. I tend to hold on to older classic bands that I really like. That said, here are the bands that I've enjoyed most since 2000:
Keane: I have all their albums till date and really enjoy their piano pop sound. Love Tom's vocals as well. I think he has one of the best voices I've heard in recent years.
Porcupine Tree: Yes I know that they started way earlier but I got into them in the 2000s. Favourite albums are Fear of a Blank Planet and Deadwing.
Radiohead: They also started earlier in the 90s and my favourite is probably either Ok Computer or The Bends. But I also quite enjoyed their output in the 2000s up until and excluding the weird King of Limbs.
Muse: Enjoyable band combining elements of Queen and Radiohead. Lately I've lost track of them though. Haven't really listened to 2nd Law. But I love what I've heard from Origin of Symmetry, Absolution, Black Holes... and The Resistance.
Tame Impala: This is the newest band that I've gotten into... during 2013. Heard Innerspeaker first and didn't like it all that much initially. But after a few listens, I was so addicted to this album that I simply had to get Lonerism as well. Then I went and listened to their 2008 EP as well. Brilliant band though they remind me of the Beatles sometimes, so not very original. But theirs is the next album that I'm most excited about, not counting personal sentimental favourite U2 of course.
Honourable mentions:
The Killers (Hot Fuss was brilliant and one of my favourite albums of the 2000s),
Snow Patrol (Final Straw and Eyes Open were both decent).