As of now (August 1st, 2015) the maximum zone number you can reach in game is 4725. Once you reach this zone, a giant angry potato with infinite health will be stuck on your screen, permanantly, or until you change zone, leave the game, and come back. There is no way to kill this potato, I've even tried using cheating devices, it just does not die. More zones may be added in the future, but there's no way to tell.

Edit: To all of the people saying it's more than this, you can only get that high by cheating, so shut up.
Edit 2: apparently y'all cant see this guide says AUGUST FIRST, so I'll say it here. Yes, the game has recieved an update and the max zone is higher now, BUT I dont play the game anymore, so I won't be updating this any further... probably.