Wii U: Dr. Mario, Wario's Woods and Adventures of Lolo are nice puzzle games. Super Dodgeball is good but it's better played in multiplayer, obviously. Ufouria is a great game by Sunsoft, with excellent graphics and a cult-classic soundtrack. Life Force is a great shmup. Gargoyle's Quest 2 is going to release soon and it's also very good.
Wii: Gradius, Zanac and SCAT are cool shoot-em-ups. Bubble Bobble and Adventures of Lolo 2 are nice puzzles. The Legend of Kage, Mighty Bomb Jack, Milon's Secret Castle and Blaster Master are considered classics. I like Princess Tomato in the Salad Kingdom but it's not for everybody. Faxanadu is fantastic.
These are all good games and you're bound to find something you enjoy in there. Google them up, see a video or two on youtube and decide which one you're more interested in according to what you're looking for at the moment. This list assumes that you included Punch-Out, Double Dragon, Kid Icarus, River City Ransom, Metroid, Ninja Gaiden, etc as "obvious ones," of course. Have fun! And that's a nice avatar you got there.