The worlds have finite size (4096x4096 blocks for the current alpha worlds, this might change until the 1,0 release). But worlds will “wrap”, meaning that if you constantly run left you will end up at the place you started from (just like in Pacman). so you don´t have to be afraid of hitting any artificial invisible walls.
That´s the plan The unprotected areas of a world will regrow into their original state (with ressources being distributed slightly different each time to prevent “ore-camping”).