Hardly any. I was talking about this lastnight and we really couldn't come up with anything near like what The Beatles, Pink Floyd etc have accomplished. Everything these days seems to be passing fads.
Even though they are 90s mostly, Rammstein are still going strong today, coming up on being in the business for 20 years. And they are the biggest international band that doesn't speak English, and a big international band period. Not everyone's taste but they have had their lasting effect on me since 1997 (it helps that I speak German). The only band that I still actually buy physical albums and DVDs for.
Talking 2000s, I can't truly think of any band that I really cared about. I listen to some, but they have no stay effect.
.....Nope, really I got nothing. Stared at my mp3 collection and couldn't say to much.