I started to comment on the Marginal Revolution picks that Allison links below, but it was getting long so decided to turn it into a post. I agree there's some good stuff in Tyler Cowen's picks, but a list like that is always designed to be a conversation starter so, FWIW, here are my two cents:
Technology I agree that the iPhone is the single the most significant technological device, but I think Google is the tech story of the last 10 years. The massive amount of information collected by Google (and to a lesser extent other search engines), and disseminated to government and the private sector, is going to exert enormous influence on commerce, culture and economics for decades to come.
To Read Agree about the importance of blogs (but not Freakonomics, which is over-rated) and that this is not really an age for fiction. But The DaVinci Code was a huge and hugely significant literary event. It is already one of the 10 best selling novels of all time (almost twice as many as the first Harry Potter book) and spent record time on the NYT best-seller list. The fact that such a bad, and mendacious, book was so popular will be seen as a sad but revealing commentary on the era.
Films Unfortunately, the same can be said about Avatar, which was technically dazzling but probably more harmful for healthy brain function than crystal meth. The Avatar technology will obviously be influential, I hope the 'ideas' are less so.
I also think the Aughts can be seen as the Judd Apatow decade in film. His sensibility has been stamped all over movie comedies of the last 10 years. Likely to remain influential in the next several years, beyond that to be seen...
Music Here's where I have to dissent from the estimable Professor. Yes, the Youtube era is important and I suppose you could say Lady Gaga is the first to achieve major stardom via Youtube. But I suspect Gaga herself is already close to peaking (one reason is she's starting to take herself seriously, always a bad sign), and twenty years from now she'll be largely remembered as a curiosity (unlike Madonna, the Lady Gaga of the 80s who's managed to stay in the news for three decades). I also think Youtube is less significant than the MP3/music download phenomenon, which has transformed the music industry in the last ten years. As for 'canonical performers,' I would nominate Jeff Tweedy and Wilco. Obviously both were making music well before 2000, but the whole Yankee Hotel Foxtrot saga and sensibility were very much of the decade.
Television This is what I know least well, but it's seems like reality TV really took hold over the last 10 years and is not going away. Paris Hilton as cultural pioneer?
What's it all add up to? For media and music, I think the over-riding themes are decentralization and cutting out the cultural middleman (e.g. the newspaper, the record company). Those trends are here to stay and mean even more do-it-yourself experimentation and creating direct links between media/music producers and consumers.
We're starting to see something similar in visual media as well, but it's in the very early stages. Youtube is still a mangy but intriguing mix of home movies, reality TV, music videos, and clips from movies and TV shows, but people are using these raw materials to create new visual cultural products. iMovie and related software are also making DIY movie-making more feasible all the time. This phenom probably won't go as far as with music and news media, because the production of visual media is inherently more capital-intensive and its 'consumption' is also more social (reading a blog or listening to an iPod at Starbucks isn't that different from doing the same thing in your living room; that's not true for watching a big screen movie). Still, I would expect to see more movement in that direction and wouldn't be surprised if, in the next decade, there is the first amateur hit movie created by and starring a cast of unknowns, publicized entirely by word of mouth and the net, and distributed exclusively (and digitally) by Netflix.