Admittedly, this first pairing is more of a crack pairing than any serious inkling I have to ship these two. But their fanbases are so large -- and terrifying -- that even if I were loath to seriously include them on this list, somewhere out there is someone currently writing the fanfiction and drawing the art (you could not pay me to link to this), and I have no choice but to add them to a crossover coupling list because of their popularity.
Is it their competitive natures that appeal to people? Their similar "Jack of All Trades" stats in their sports games? Perhaps it's the contrast of the red and the blue.
I don't know. I don't care. Perhaps in a PG universe, I could see the appeal -- alas, as long as rule 34 exists in the universe, I will never do an image search for Mario and Sonic ever again.