Well I'd say in the US anyway that the early 00s ('00-'01 and some of '02) was a lot of the same late 90's soft rock, teeny boppers, and R&B (i.e. Destiny's Child), which was followed by a (very) brief resurgence metal and punk ('02ish-'04) such as Linkin Park and Yellowcard, P.O.D., Evanescence, New Found Glory, Good Charlotte, and their ilk. At the same time we have a new sort of hip hop arising (at least to my ears hip hop of '02 and later sounds like somewhat of a departure), and so that's people like Fat Joe, R. Kelly, OutKast, B2K, etc.
After that was the rise of emo and other forms of throwback music like garage rock and punk-gone-straight Green Day (so that's '04ish-'07) and that includes Panic!, FOB, The White Stripes, Franz Ferdinand, the Killers, RHCP (i.e. Dani California), etc. At the same time we had what will probably become some of the decade's most recognizable hip hop and R&B tunes (and I consider it to be the decade's best, but you're free to disagree of course): Yeah! by Usher, Golddigger by Kanye, Crazy by Gnarls Barkley (I know it's closer to soul), Apologize by Timbaland and OneRepublic, Justin Timberlake, etc. For the end of this era I'd point to songs like Hey There Delilah, Paper Planes by M.I.A., Handlebars by the Flobots, etc.
And then we have the 2008-2009 era, which I consider some of the worst and weirdest of the decade. This is Lady GaGa, Rihanna, the Black Eyed Peas' new (terrible) electro-hop sound; I remember at one point these artists were labelled on Wikipedia as the rise of "nu-disco." Also I feel like there was a brief period in which indie music became pretty popular, but I'm not sure if that's a product of my going to college, my piqued interest in indie around that time, or something else. The most solid evidence I have for the indie resurgence is in film of the late 00's, such as "indie-style" films such as Juno and Where the Wild Things Are, in which such music is featured very prominently. I also think I remember a couple of "dance" groups such as Metro Station becoming pretty popular around 2008 or so. That's the best I've got for the latter era though, as I have no idea what was happening in straight-up pop, country, and rock.
As for 2009 in particular, this is what I've got: Lady GaGa's fame continues its ascent and is joined briefly by Green Day's 21st Century Breakdown, a smaller hit than its predecessor, and then the death of Michael Jackson. At this point my trail through popular music at the time gets hazy amid all the Jackson hype, and then I remember some Taylor Swift, and that the #1 hit going into the new year and decade was Hey, Soul Sister by Train, which stayed very high in the charts well into 2010.
This is all the product of intense research and really making an effort to expose myself to popular music when I got into college. If anyone has found any holes that need to be filled in or I'm just dead wrong about something, the help would be greatly appreciated.