Looks like Microsoft is working hard towards that "Live Anywhere" goal.  Speaking at TechEd Middle East, Microsoft's Eric Rudder showed off playing a game on the PC, then switching to a "Windows series phone" (ie: Windows 7 Series Phone) and then finally to a Xbox 360.  The whole time he is playing the same game and it's picking up where he left off with the previous device.

Granted the game he is playing is a simple platformer, but who know what good developers can do with this in the future.  A video of the demonstration is below.