The next big toy after Tickle Me Elmo was Furby. The Furby spoke a language called "Furbish," but also had several pre-programmed phrases. It would "talk" in response to sounds. Or, put two (or more) Furbies near each other, and they would "talk" to each other, thanks to an infrared port between the eyes. There are many versions of Furbies, including the "Gizmo" from the film Gremlins.
And if you can't get enough of the little furry things, behold the Furby Orga