Even Been to This Free London Yew Maze?

A maze where the goal is not on the edge of the maze. In this case, the goal is in the center.

3-dimensional mazes (which have bridges or tunnels) also often cannot be solved with this rule.

The left hand rule assumes that the end is on the same "cycle" as the entrance:

   --E--
  |     |
  |     |
   --S--

if the end is instead on a different "cycle", it won't work:

   -------
  |       |
  | -- -- |
  ||     ||
  ||  E  ||
  | ----- |
  |       |
   ---S---

Hopefully this makes sense. I'm sure there's a propper phrasing of this in topology, but I don't know it.

Yes, in a maze without cycles the left-hand rule will take you through every part of the maze, guaranteeing that you reach the goal.

Of course in a maze with cycles you might still reach the goal, but it's not guaranteed. For example there's a cycle in Hampton Court Maze, but the left- and right-hand rules both get you to the goal from the entrance.

Any maze with a wall that loops around itself.

They are referred to as "multiply connected" in the literature on mazes. Essentially, this is the mathematical way of saying that there are "islands" of hedge, not attached to the perimeter.

Nice, but they could have used some more contrasting color for the maze paths...