This excellent tutorial on how to create art in the “8-bit” mode offers wonderful insight into an obscure genre of visual expression. It lays down many of the aesthetic principles that underpin the rendering of convincing looking objects with restrictive color palettes and limited resolution. It was written by the artist Arne Niklas Jansson, who has a knack for making this very particular technical proficiency sound like an extension of more traditional forms of art.
In a way, pixel art is like analog art scaled down, but the pixel space can force certain exaggerations, detail reductions, alignments, graphical simplifications and iconographies. It has to be adapted so it’s readable, but a lot of the functionally effective ideas and wisdoms from analog art (be it more abstract graphical ideas or realistic-ish painting styles) can be ported and applied, I think.
However, when a human is presented with the very structural pixel art space she tends to ignore that and go into telephone doodle mode, making patterns, symmetries, outlines around outlines, little pointless ramps of colors, and other needless additions because the spatial forms somehow encourage it. When I fall into that mindset it helps to retract my mind from the pixel space and imagine the sprite/tile more like a regular painting done with a very large brush. Each pixel is very important as it actually corresponds to a large blotch of paint rather than a single tiny pixel. I think pixel art is very much about knowing where to make sacrifices of detail due to the scale, and how to make each pixel do double duty.