Sopranos ran 1999-2007. But that first season (still the show's best) does show its 1999-ness in quite a few places. So that one's toeing the line.
Comic book movies first boomed in 2002 with Spider-Man but those are still going.
John Mc already mentioned Lost.
Does anyone remember the short time period in the middle of the decade when girls were all wearing tiny little pleated skirts?