Today, when I visited youtube.com, was very happy to see the application supporting Kannada locale.
To get your favorite site in your own language, always make sure to set the locale that you like.
On Mac, Open System-Preferences -> Language & Text -> Click Edit List and Add Kannada. Make sure ಕನ್ನಡ is first in the list.
On other systems, this has to be done specifically in browser.