I'm gonna go ahead and say it: robots. I wish the answer was more original but I'm afraid it ain't.
This is what is being developed right now. Social robots for kids, meant for social training (autism...), special care, or general education. It is more engaging than "lifeless" toys (ie. not social), more efficient than TV at teaching, more attractive than anything else.
Hasbro's Furby is on the cheap end of what already exists. For more elaborate stuff, the Personal Robots group @ MIT Media Lab has some good examples:
These — in their future versions — will basically be you best friends, your personal teachers, your health trackers, soft, fluffy and squishy for night time and shiny and fun for activities. And all that, specially tuned to the kid's needs because it learns from social interaction and cues.
So what will they do with these robots? That's the hard part I believe. Probably very "human" games. Things that feel very natural to us because evolution meant for play to be a learning activity. But probably the robots will be able to project a 3D environment around the kid to enhance both the experience and the teaching, narrate a story, add hidden tests and activities, put in a few words of another language...
If you want some specific examples of games, try and think about what needs to be worked on as a child. Motor skills, social skills, logical reasoning, all sorts of life skills (confidence, self awareness, creativity, ...), and any "bonus" skill you might want to throw in (music, 2nd language, programming, ...). And embed all that into the most engaging activities for kids, usually some sort of open-ended game like the imaginary adventures you might have had in your backyard as a child. IMHO, the result of all that would be some open ended improvised game led by the companion robot in order to tune the level of the various variables to the child's skills.