I remember the talk of how Madonna and Michael Jackson were killing music when I was younger. And how Guns 'n' Roses and Metallica were going to make us all grow up to be serial killers. I remember hearing the laments of people who wondered if the music died in the 80s (or elsewhen if you believe Van Morrison).
Pop music is seldom appreciated in its time. Influence needs time. However, I think many bands and singers nowadays will have lasting impressions on tomorrow's music. I realize that a lot of people have put up favorite, obscure, artists and that's all well and good but if we look at people who did get played on the radio, because that's where they gain influence, even thaen I think there are artists worth noting, even if you don't like their music:
Eminem [http://www.youtube.com/watch?v=j5-yKhDd64s]: already stated a couple times, but he changed the face of rap and hip-hop.
Timbaland [http://www.youtube.com/watch?v=XewBty95JVg]: seriously, this guy has his fingers in pretty much every good Hip-Hop pie. He's the Quincy Jones of the last decade.
Apocalyptica [http://www.youtube.com/watch?v=VyqLl0XoMTI]: Redefined metal. Going from a metallica cover band to a stadium selling phenom with amazing music and guests from all over the world.
The Roots [http://www.youtube.com/watch?v=ojC0mg2hJCc]: (slightly more obscure) Probably the best hip-hop group out there. Outkast and the Black Eyed Peas can suck it

Tool [http://www.youtube.com/watch?v=EiR1hmpk-x4]: The thinking man's prog-rock. Musically, probably the most sophisticated band out there now. Sure, started in the 90s, but still relevant today.
Jamiroquai [http://www.youtube.com/watch?v=f7wELq4Sdxg]: Had a quick hit in the states in the late 90s with Virtual Insanity, but has exploded worldwide in the oughts. A mix of funk, disco, acid jazz and electronica, these guys are great.
Lacuna Coil [http://www.youtube.com/watch?v=CXq6id9gvxA]: Best of the "melodic/symphonic" Metal genre (more populist than Nightwish, Sirenia or Within Temptation) that found a bit of fame in the states after a spot on Kimmel and a cover of Depeche Mode. Absolutely huge overseas.
Daft Punk [http://www.youtube.com/watch?v=oGECJP3phyY]: THE techno/electronica group. No other has infiltrated popular culture more (Buy it, Use it, Break it, fix it, trash it, change it, melt - upgrade it...), none has been as popular, and arguably none has been better.
Juno Reactor [http://www.youtube.com/watch?v=ZiSsBY-ehvU]: THE answer to Daft Punk, and a completely different take on techno. Fusing electronica and world music in a way that brings together the cutting edge and the ancient. Got wildly popular on the backs of the Matrix Movies. Both groups started in the 90s but found their popularity more recently.
These are several of the bands who were popular in the oughts, who had radio play and who I believe will be some of the better influences down the road. Remember, not everything now is Ke$ha and Miley Cyrus, just as everything in the 80s wasn't Debbie Gibson and Whitesnake.
Edit: linked to some examples. Honorable mention goes to: Yoko Kanno [http://www.youtube.com/watch?v=8lomNiMATjk], and many others. Some links have NSFW language, so click with caution.