Most of the projects in this vein are defunct, including the Tux Droid, the original Furby, the original Teddy Ruxpin, and the Nabaztag rabbit.

I always felt the story of Felix Gallo's "Poppet" project at Data General was interesting: http://metatalk.metafilter.com/13606/#384503

An original Teddy Ruxpin doll would probably have been the easiest to hack, replacing the cassette tape with a stereo audio input and generating the pulses necessary to animate him at your discretion: http://www.illiop.org/workings.html

The Nabaztag rabbit has been resurrected a few times, it looks like you can buy a new "Karotz" model for US$130, needing only a plush exterior: http://store.karotz.com/product/22/karotz

You could stuff another sort of mechanical toy, like a RoboSapien RC robot, into a stuffed animal: http://www.youtube.com/watch?v=e_WJ23Zg1Rg

There's also a new startup named ToyTalk, which seems to be doing something in this vein: http://www.toytalk.com/

You might find it easier to start making something that's not quite as complicated as an animatronic toy. Soft electronics projects and startups have been around for years, with shirts that hug you back and pillows that light up:

Pillow Talk: http://www.joannamontgomery.co.uk/littleriot/?q=node/11

Chatter Pillow: http://sternlab.org/2006/11/chatter-pillow/

For making one yourself, books on soft electronics might be useful.

Making Things Talk: http://shop.oreilly.com/product/9780596510510.do

Fashioning Technology: http://shop.oreilly.com/product/9780596514372.do

Instead of regular Arduinos, you can use sewable electronics specifically designed for this, like the Lilypad, which you can get at SparkFun, in their e-textiles category: https://www.sparkfun.com/categories/204

Adafruit also has their own line, just launched, called FLORA: http://www.adafruit.com/category/92

There are lots of "robots lite" projects you could wrap in fuzzy fabric, too, like this animatronic head: http://www.kickstarter.com/projects/jeffkessler/tj-an-animat...

It really just depends on how complicated you want to get with it. Depending on your experience, it might be best to start small, working through the projects in those books.

The book "Making Things Talk" (O'Reilly) is a great way to start:

http://oreilly.com/catalog/9780596510510/

Art of Electronics is a very good book, but if you want to learn from a fun / programming point of view I highly recommend "Making Things Talk", by Tom Igoe.

http://oreilly.com/catalog/9780596510510/