There is a classical labyrinth in a quite special form: The man in the maze. It is to find above all on the baskets of the Native Americans in the US which have presumably also developed this type.
It is round, but the goal is not in the middle. If one looks exactly, one recognises the four points of inflexion of the classical labyrinth. They also mark four corners of a square.
The subdivision in 8 segments is new, they also allow to think of the spokes of a wheel. Thus gets in addition a movement towards the centre and away from the centre. The order of paths is again 3-2-1-4-7-6-5-8; well-known from the classical type. The “path changes” always occur on the 9th and 10th ring. The 11th is as it were the stationary pole or the hub.
You can see a Flash animation on the website mymaze.
If you would like to build such a labyrinth: Please, here you may find the layout drawing as PDF file to look on, to print or to copy.
Postscript from March 2012:
Meanwhile I walked such a labyrinth in the Netherlands. You will find the post of this visit here:
Dolen in dit doolhof: The Willow Labyrinth at Ijsselstein(NL)