Those are called cartograms (TIL), and there are loads of them here:
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Speaking of population maps, here’s my favorite map of New Zealand, titled Nobody lives here.
And my preferred projection from the XKCD comic is perre quincuncial. Because it’s great.
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I thought the Authagraph projection was supposed to be the most accurate?
Orthographic?
Depends on what you mean by “accurate”. 
It’s great for the area immediately below the point of projection, nearly useless 90 degrees away.
Tissot’s indicatrix of deformation is a good way of showing how a projection distorts the terrain - by their nature any projection will be imperfect.
One of the things that occasionally exercises my mind is procedural generation of maps for alien planets in SF RPG. No great precision is needed, but I think an approximation to an equal-area projection is wanted. Or rather, six.
- You want one projection for the case when the polar regions are frozen and sparsely occupied, so that most activity takes place in an equatorial belt.
*A different projection might be best when the polar regions are mostly icy and the torrid zone too hot for comfort, so that most matter of interest is in two mid-latitude bands. - A third is wanted when the equatorial belt is too hot for habitation, and activity of interest is mostly confined to two temperate polar regions.
- And I think that maybe a fourth projection might be needed for planets with effective meridional transport of heat, that are habitable from pole to pole.
- Then you need a fifth for cool synchronously-rotating worlds where habitation is confined to the centre of the sunny side
- Beside maybe a sixth for humid temperate synchronously-rotating worlds on which the sub-solar zone is too hot for human habitation but a ring around it on the sunny side is not too dry and windy.
Any suggestions?
ObXKCD: 977.
I think there are two major things going on here.
- Overall, what is the habitation pattern? For this, I think, you want the same projection for each planet, so that readers can easily compare them. And there are worse options than the icosahedral projection I first saw in Traveller books: it reduces some of the upper-latitude distortion at the cost of making the poles near-illegible. (The GURPS Space Planetary Record Worksheet has separate polar cap maps.)
- Once you’re on the planet, where can you go? This is the map a travelling local would use, that concentrates on the interesting places.
I’m not going to link to the west wing here, but just wanted to add the map makers love putting themselves at the centre of maps.
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Yes, I love USA origin world maps, how they don’t care about splitting the largest, most populated continent in the world to fit the Americas in the middle
Its always worth linking West Wing
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