According to Co optimus anyways there are roughly 16 wii games that support online gameplay.
And here they are:

The Last Story Rated 80 at metacritic
Rock Band: AC/DC Track Pack Rated 55 at metacritic
Monster Hunter Tri Rated 84 at metacritic
The Beatles: Rock Band Rated 89 at metacritic
Guitar Hero Smash Hits Rated 74 at metacritic
Final Fantasy Crystal Chronicles: Echoes of Time Rated 64 at metacritic
Band Hero Rated 79 at metacritic
Green Day Rock Band Rated 76 at metacritic
The Grinder NOT RATED at metacritic
Battalion Wars 2 Rated 75 at metacritic
Guitar Hero 3 Rated 86 at metacritic
Endless Ocean Rated 72 at metacritic
Mario Strikers Charged Rated 79 at metacritic
Super Smash Bros. Brawl Rated 93 at metacritic
Guitar Hero Aerosmith Rated 73 at metacritic
Valhalla Knights: Eldar Saga Rated 35 at metacritic