Probably the most generic list ever Dragon Ball Z, Yu-Gi-Oh, Sailor Moon, Inuyasha, and Death Note. A (somewhat) less generic list Higurashi no Naku Koro ni, Black Butler, Elfen Lied, Azumanga Daioh, and Hetalia: Axis Powers
That makes no sense at all. If they were the best, people would want to watch them thus they'd be on TV.
Well it's true all the best anime is not broadcast on American at least. There is an anime for everyone try Cowboy Bebop, Haruhi, and others listed in this thread. They are far better than any broadcast on American TV. The only good anime I know that was broadcast in North America is Black Lagoon on G4 Tech TV Canada because they had to meet the 60% Canadian content regulations.
Higurashi no Naku Koro ni? Happens a number of times. And yes, Kara, anime on TV is usually very shitty. I'd say that a good 99% of all anime is shit. But anime itself isn't shit because it's just an artistic medium.