1.) Nearly all of the Nintendoes, including Virtual Boy, a Sega Master System, Game Gear, Genesis, (with 32X,) Saturn and Dreamcast, Playstation 1, 2, and 3, Xbox Original and 360. There’s probably more.
2.) My favorites are Platformers, JRPGs, Action, Adventure, Beat-em-Up and Puzzle, as long as they have interesting gimmicks or gameplay mechanics. My least favorites tend to be WRPGs, FPSes, Sandboxes, and Simulations.
3.) I’m hoping we get into more obscure titles. Perhaps something like Jet Set Radio.
4.) Either Wario Land 2 or 4. Wario Land 2 is easy to pick up and play – in fact, you can’t even die in it. It also has multiple paths and endings, so two people could play and get very different story-arcs. Wario Land 4 is a bit more of a straight shoot, and has a heart system. Wario Land 4, I think, might be the better of the two, but I’m not sure as to availability for either.