It's really the inbetween work that's done overseas. Stuff like animatics, model sheets, and key frames are still done here. I mean, Japan frequently outsources to Korea nowadays, and anime is still called anime.
Anime's a tricky term. Anime is only called anime in Western countries, where as the term means all animation in Japan. But yeah. Outsourcing. Weirdest thing is that Titmouse supposedly supplied some animation for Space Dandy. A western studio that Japan outsourced to. Then there's the flash based cartoons which, for the most part, are done in Western countries. There are ones they outsourced to, like Mucha Lucha. That's one of the good things about Flash based animation. It keeps it homegrown, at least. I'd assume that if Filmation were still around, they'd go that route.
But I really like the look of an outsourced series, especially if it's outsourced to Japan. Few are today. I know the new Thundercats one was, same studio that did TFA (thoguh I have to admit, they just had some trouble with the look of the series, and whoever would eventually do Ben 10 Omniverse would have done a better job... same artist designs). There are also a few cases of DC DTV projects (it includes Gotham Knights, but TMS did one of the Green Lantern ones, and another studio did the one shot Super Friends Imaginext pack in DVD). But there's just something about the TMS animated Ducktales episodes...