Mine is Buckminster Fuller's dymaxion map: https://en.wikipedia.org/wiki/Dymaxion_map

Great for showing the relative sizes of continents (and also visualizing how all the continents are nearly one contiguous landmass), at the cost of chopping up the oceans.

Second favorite is the Peirce quincuncial map: https://en.wikipedia.org/wiki/Peirce_quincuncial_projection , which tiles the plane.

The Dymaxion map is very interesting, I was a bit surprised just how connected the continents actually are.

Pangea theory is much more obvious when you look at that map.

Also it is interesting that it is as if the whole "land" of the world is basically a big island in the middle of the ocean.

That looks pretty tough on New Zealand.