Usually considered an extension of the 1990's for American culture. Pretty much had the same feel of the past decade, but with a lot of political and economical trouble.
Many music stars and bands who were popular in the mid-late 90's continued their popularity, with some new emerging stars who sung in the same style. The boyband fad died in 2002, with the end of NSYNC and the hiatus of the Backstreet Boys.
Many popular shows from the late 90's continued or aired in reruns through the period. Reality TV was popular, but it wasn't usually scripted. Anime dominated the animation scene. In addition, 90's shows, which were either running or in reruns, remained popular. Adult cartoons became popular.
Politically, the early 00s was overall a horrendous time. Bush was inaugurated in 2001, followed by the 9/11 and anthrax attacks and the War on Terror later that year. The Iraq war in 2003.
The economy wasn't doing too well. The dot-com Bubble burst in 2000, leading to a recession in the 2001-2002 years, though it wasn't as bad as the late 2000s or 1930s recession.
Video games systems included the original Playstation, the PS2, Xbox 1, Dreamcast, Game Boy Color and Game Boy Advanced. Online gaming started to become popular. 2D gaming was accepted for the portable systems, and portable remakes of many 80's and 90's classics. Home consoles usually had 3D games, but there were compilations of classic 2D games.
It wasn't perfect, but many are starting to reminisce on the time today.
Some stuff from the early 2000s:
Music-NSYNC, Oasis, Madonna, Michael Jackson, U2, Britney Spears, Ashanti, Nelly Furtado, Nelly, Black Eyed Peas, Backstreet Boys, Simple Plan
TV (Live Action)-Everybody Loves Raymond, Survivor, Big Brother, Malcom in the Middle, Frasier, Friends, Coronation Street, The Guiding Light, Lizzie McGuire, That's 70's Show
Cartoons/Anime-Hey Arnold!, Angry Beavers, Spongebob, CatDog, Pelswick, Pokemon, , Inuyasha, Mon Colle Knights, Medabots, Beyblade, Cowboy Bebop, Courage the Cowardly Dog, Powerpuff Girls, One Piece, Gundam Wing, Trigun, Yu Yu Hakusho, Saint Seiya (Knights of the Zodiac), Dragon Ball, Dragon Ball Z, Digimon, Teenage Mutant Ninja Turtles, Monster Rancher, Spongebob, Family Guy, South Park, King of the Hill
Events-Sydney Olympics, Queen's Mother 100th birthday, Bush, 9/11, anthrax, recession, Chinese economic boom, Salt Lake City Winter Olympics, Euro enters circulation, Enron, Iraq war
Video games-Spyro, Phantasy Star Online, Crash Bandicoot, SOCOM, Kingdom Hearts, Halo: Combat Evolved, Megaman Battle Network, Super Mario Bros. 2 (remake), Final Fantasy IX, Final Fantasy X