Mercator v Reality
With a human face
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I kinda like the Kavrayskiy VII projection. It's similar to the Winkel triple but it looks more natural to me, like a 2D Google Earth.
Eckert IV is mine, which is quite similar visually. It has the upside of being equal-area, but the downside of squashing the poles a bit more. Sadly both of us suffer the injustice of being excluded from that one xkcd comic
It looks cool!