Super Smash Bros. Brawl, Mario Kart Wii, and Goldeneye are, to my knowledge, the three most popular online multiplayer Wii games. As for Wii U... ... ... well, I've got next to nothin'. The latest Assassin's Creed continues with supplying the great multiplayer that started back in Assassin's Creed: Brotherhood, but said multiplayer experience is rather niche. Not quite as widely appealing as the aforementioned three games, although those who enjoy it tend to love it. Myself included.
Not sure 'bout the U, but this should help narrow down your hunt for online Wii games. Mind you, that's a list of online games, not online multiplayer. But 'ey, it'l still save you some time.