I have to admit, my all time favorite gaming system was the Super Nintendo. It doesn't have the graphical power or the sound tracks of todays gaming systems, but the games for it were incredible. I felt like playing those games constantly, which is a rarity with some of the next-gen console games.
A few of my all time favorites:
Rock and Roll Racing - Great gameplay and soundtrack (even though it is a midi soundtrack). The commentators are fun, though occasionally annoying.
Mario Kart - Good single player game, great multiplayer.
Super Mario World - Many wasted hours on this one. After all, I had to finish all of the levels and get the star.
Super Punch Out - Just a great all round game. A lot of fun to play and very easy to get addicted to.
There's more, but I'm going to wait to hear your responses.