If you are in the frontier, the border is practically unlimited. If you are in the wastelands, you hit an invisible barrier and are warned in chat that you have reached the edge of the map. Not sure of the exact wording.
in minecraft technically there is a border after 30,000,000 blocks then it still generates terrain but it has no phsyics
If you reach the end of the miencraft world (commonly known as the far lands) you will run into an invisible wall. I tested this on sp using the tp command. It isn't as exciting as in previous versions, but it does prevent you from having a lag attack.