Some of these consoles had thousands of games released for them and my particular scope is comparatively narrow. Not being the foremost expert on everything, I've made all of these recommendations based on personal experience, games my friends from school liked, games I've seen played, or, failing all that, contemporary sales figures. Also, the limit per page is 15 games, plus 5 honourable mentions. Doing this keeps down complexity and prevents me having to constantly come back and add more games. I'm assuming that you'll use the list as a jumping-off point from which to get into a particular console and then, from there, find games that you like better than the recommendations. I am not able to divine everybody's favourite game from sheer clairvoyance, but, plainly, if you have favourite games for a system, then you're already familiar with it and thus are not my intended audience.
"Why 15? Why not 20? 50? 100?" Because 15 is how many games I had for Nintendo 64 and GameCube. It's enough to assuage most forms of boredom in the immediate moment and serve as an introduction to an unfamiliar system from which you can branch out and try different games.