I was alive for a couple of them, but I never had a Game Boy.

Try choosing a color palette with a range of values but unnatural colors and selecting the ordered dithering, 2x2 matrix. Isn't it nice? I wonder how hard it would be to do as a build step in a static site generator. (Oh, man, you could theme your image assets to match swappable site color schemes... has someone done this? Someone who cares more about swappable color schemes than I do should do this.)