As someone born in '89, I remember the 00s from a cultural standpoint being from 1998-2007, not from 2000-2009.
1998-2002 was the first half of the real 00s. Post-grunge was at its peak with Foo Fighters, Matchbox Twenty, Semisonic, Staind, Lifehouse, Puddle of Mudd, The Calling, and of course Nickelback and Creed.
There was also the pop music from that time. It sucked, there was NSYNC, Backstreet Boys, Britney Spears, Jessica Simpson, and Christina Aguelera, who were just intolerable. At least there was good pop-rock and pop-punk bands like Sugar Ray, Green Day, and Blink 182. Rap gave us Eminem and Nelly. Eminem especially, was just awesome back then. Nu metal was huge then, like Linkin Park, Korn, Slipknot, Papa Roach, Limp Bizkit, etc.
This was also when I noticed most people starting to use the internet. Although there was Windows 95 in use from 1995-1997, the internet didn't really start taking off until 1998 with Windows 98. That's when I started noticing everyone using the internet.
Also, in the gaming industry, this was when the PS1/N64 were still going strong, but 128 bit consoles (DC, PS2, GC, Xbox) were being introduced in this era.
I think 2003-2007 was the second half of the real 00s. This was when post-grunge was dying off to make way for gothic/emo pop-punk and alternative rock. It started kicking off with Simple Plan and The Killers, and was in full swing with Green Day's "American Idiot". In this era, we had bands like Taking Back Sunday, Fall Out Boy, Panic! At The Disco, My Chemical Romance, 30 Seconds To Mars, Three Days Grace, and Red Jumpsuit Apparatus.
Emo was especially a fad back in this time period, too many people with dark black hair, tight jeans, a lot of piercings, many of them they bought at Hot Topic.
Rap music went downhill fast in this era thanks to the Dirty South takeover.
Most people switched from AOL dial up to broadband around 2005, and MySpace started taking over. MySpace will especially be remembered being associated with emos, since there was a flood of them on MySpace back in 2005-2007.
As for the gaming industry, this era was still during the sixth gaming generation, but the seventh gaming generation consoles were being introduced in this era.
2008 is when the 10s really started. Electro-pop became popular, Lady Gaga and Katy Peary came along. The 10s has been so far the crappiest decade ever. The 00s was the last good decade. I wish I could go back to the 1998-2002 period, hell even the 2003-2007 period.