I played all the time when I still had mine (it's in another state for the moment). One game I'm horribly addicted to that makes me kind of glad I don't have it right now is Final Fantasy Crystal Chronicles: My Life as a King. A downloadable game with some extra fluff DLC, it's a kingdom-building micro-management game and it's extremely hard to put down once you get going in it. You play as the king of a country and start building up your castle town while setting "behests" for adventurers (white mage, warrior, black mage etc.) you recruit into your employ. They go out and do all the fighting, while you make nice with the townsfolk and build stuff with the materials they bring back. I absolutely love that game...
Can't forget Okami, Twilight Princess and Skyward Sword, Chocobo's Dungeon, Warioware, Mario Galaxy... there are so many great games and I find the wii controller so fun to use. I never want to give up my Wii XD