I do. I love the fact that technology has made it available for me to watch and listen to all the old shows/music I like at a relatively low price.
This century has also given me some artists that I really enjoy:
-Gorillaz
-LCD Soundsystem
-Coldplay (yeah, I like Coldplay. Sue me.)
-Panic! at the Disco (I hate the emo look they had during their first album, it just looks ridiculous in my opinion. They sure know how to write a song with halfway clever lyrics and a catchy hook, though. Call 'em a guilty pleasure.)
-OK Go
-Passion Pit
-Foster The People
-Gotye
-Fun.
(I also like listening to a lot of indie rock/indietronica. Sue me again.)
And many other critically-acclaimed and well-liked artists that I haven't even listened to yet:
-The White Stripes
-The Strokes
-The Black Keys
-M83
-Bon Iver
-Of Monsters and Men
-Mumford and Sons
-MGMT
-Kendrick Lamar
-The Postal Service
-Capital Cities
-Mordecai and the Rigbys
Speaking of Regular Show, that proves that this century also created some awesome cartoons like Adventure Time, Teen Titans, Foster's Home For Imaginary Friends, Avatar: The Last Airbender, Danny Phantom, My Life as a Teenage Robot, Fairly Oddparents (for the first few seasons), Invader Zim, Dan Vs., and MLP:FiM. (You might say that last one's debatable, but I honestly think it has a certain charm and innocence to it that most cartoons don't have anymore.)
I've also heard that such critically-acclaimed shows such as Mad Men, Breaking Bad, and The Walking Dead have high ratings and large fanbases. (I've never seen either of them, but I will...eventually!)
Sitcoms like The Big Bang Theory, How I Met Your Mother, Two and a Half Men, and Community have been getting the same treatment (and I can safely say the middle two are quite funny...I need to watch more TV, dang it.).
'90's kids don't know what they're missing.