Your Friendly Ban Hammer-er
They probably use Maya. It's the most widely used 3D creation software out there. Anime studios still either make anime the old fashioned way or use software's now. Flash can be used to make animation and if you take the time to learn it, you can definitely create something similar to those animations you see broadcast in Cartoon Network and so on.
From what I heard from a friend who works in animation, he use Abode After Effect to finish the animation touch (and the animation itself). He uses Maya to make the animation, but after all the 3Ds done, he still use After Effect.