That'd be interesting- the first thing that came to mind for me was House, M.D. and Glee.
House: I could see this series with the same format, but with anime-stylized character designs for some reason.
Glee: I could see this go more as a Ruby/Spears type animated series with extra, extra cheese.
Now, if we're talking about older shows, like from 20 years ago, I could easily see a Family Matters animated show, with Steve Urkel causing more mishaps to the Winslow residence than usual.
I can also see this happening to Saved by the Bell, but it'd be called the Marvelous Misadventures of Screech.