I admit that's a tough question to tackle. But, here are some of my favorites thus far.

The Black Keys, The Bad Plus, Garaj Mahal, The John Butler Trio. . .

tomahawk and jaga jazzist

For some reason I thought A Livingroom Hush was released in 1999...but sure enough, 2001. Put me down for Jaga Jazzist as well

I forgot about Tomahawk. Yeah!!!

I don't know much about Jaga Jazzist, I'll have to look into that one. I've seen the name around.

technically jaga jazzist has been around since '94 but according to the rules in this thread their influence didn't start spreading until 2000 so they're all good

that is a weird to understand rule then. I mean, influence is a kinda hard thing to define isn't it?

think of it like this. was the band know outside of its hometown before 2000? 'the dears' have been around since '95 but before they released 'the end of a hollywood bedtime story' in 2000 very few people outside of montreal knew who they were.

in this order, strokes, libertines, and brmc.

I forgot to say the Strokes, although they've already been mentioned several times.

Five For Fighting...excellent and sometimes profound lyrics as a part of great songwriting in general...good musicianship...beautiful production...

I can't think of anyone who comes close.