Any show from the 2000s decade. Any show that also aired in the late 1990s but continued auring in the 2000s counts too (for example, Will & Grace aired in 1998, but had more episodes in the 2000s, making it part of the 2000s decade mostly).
The most notable 2000s shows include Breaking Bad, The Office, SpongeBob SquarePants, Family Guy, South Park, Doctor Who (2005), Will & Grace, Grey's Anatomy, How I Met Your Mother, The Sopranos, Malcolm in the Middle, Six Feet Under, Dexter and Supernatural.
I hate when people tell me Family Guy is a 90s TV show just because it aired in 1999. While it technically is, it's mostly a 2000s TV show considering how it aired most of its episodes in the 2000s. That would be like saying The Simpsons is an 80s TV show even though the first episode aired in December of 1989 and the majority of the episodes aired in the 1990s.