TITLE: Undecidable puzzles
QUESTION [13 upvotes]: There are plenty of popular NP-hard puzzles,
for example, generalized Sudoku ($n^2 \times n^2$-board), Flow (I cannot give a source for this), Minesweeper, etc.
Recently, I read a bit about aperiodic tilings of the plane, and it is undecidable 
whether a set of tiles can tile the plane or not, since there might be aperiodic tilings. I do not really consider this problem a popular game you would find in a newspaper.
So, my question is this: what puzzles/games are there that are undecidable in general?
The Post correspondence Problem, (PCP), is undecidable and this has a very "puzzle"-feel to it, so I would say this game could qualify.
Perhaps some generalization of the board game Roborally on an infinite board,
would lead to some type of undecidability, that is, there is no algorithm that given a RoboRally configuration produces the resulting configuration after all rules have been applied?
As a funny note, the sand-box game Minecraft allows the user to make circuits, making the game (in theory) Turing complete.

REPLY [4 votes]: A recent (after the question was posted) arxiv preprint
proves that Magic the Gathering is Turing-complete.
The abstract states:

This shows that even recognising who will win a game in which neither
  player has a non-trivial decision to make for the rest of the game is
  undecidable.