I actually haven't seen much anime on television. I didn't know Disney had any anime on, though I hardly ever watch that channel so I probably just haven't seen it.
The only ones I know of are...
-Cartoon Network/Adult Swim (Saturday late night) has Full Metal Alchemist, Ghost in the Shell, Bleach, Cowboy Bebop and I think they're still playing InuYasha.
-Nicktoons Network will be having Dragon Ball Z Kai and has Avatar: The Last Airbender (not technically anime, I know, but it's something)
-Disney XD used to have Oban Star Racers (again, not technically anime, but was still pretty good), but no longer has that show on. Not sure if they have anything else on now...
-On Demand has a few anime series under "Funimation Anime", though you have to see it fast as most episodes only stay on for about two weeks before they're rotated out. And the selection can soemtimes leave something to be desired. They are free, though, and also have some newer series (new to the US) that you pay for.
Does Cartoon Network have any anime on during the day? Ever since they canceled Toonami I don't think I've seen any...