My very favorite map projection is the AuthaGraph map: http://www.authagraph.com

It is a novel (I would say amazing) map projection that manages to retain proportional landmass size by using an "ioso-area-mapping" technique. It maps the sphere to a tetrahedron and then slices and unfolds that tetrahedron into a 2d plane.

The method places all of the continents into the map (proportionally!), while also being able to tessellate (so you can move the "viewfinder" to focus on different map subsections without changing the overall map). It's easier to see than describe. The "4" link is an example of modifying the "view" of the tessellated surface to create maps that focus on particular regions.

The downside is that "north" and "south" are rather arbitrary points on the map, instead of being at the top/bottom.

It is still by far my favorite 2D map projection!