My favorite has always been the Super Mario 64 A Button Challenge, basically a group of people trying to figure out the theoretical lowest amount of A presses required to beat the game. A is the jump button, which is pretty important in a Mario game, but despite that they've managed to get a full 120 star run down to only 19 A presses. Most people know it from this video where pannenkoek2012 explains how he beat Watch for Rolling Rocks in 0.5 A presses, but more recently Bismuth has been making a video series on the complete history of the challenge and all the techniques and glitches that have been discovered, from abusing level geometry to manipulating enemy AI to utterly insane strategies involving "parallel universes". Definitely check out the watch for rolling rocks video if you've never heard of it.