Well since you asked for online capable games,
http://en.wikipedia.org/wiki/List_of...nnection_games
Much longer list than I thought, but the fact it needs a list unlike PSN and XBL is the story.
I have Batallion Wars, Smash, Kart, Excitebots, Turtles Smash-Up, Medal of Honor Heroes 2 and The Conduit.
For WiiWare,believe only Dr. Mario, Bomberman and Onslaught.
I will probably pick up the Capcom Vs game. And at some point I want to pick up Mario Strikers charged as well.
As for recommended titles:
Smash Bros Brawl
Mario Kart Wii
Twilight Princess
Metroid Trilogy
Mario Galaxy
No More Heroes, if you into that
Punch-Out Wii
Excitebots (really underrated game)
House of the Dead: Overkill, if you like rail shooters
Games worth checking out, but may not be worth buying:
Batallion Wars 2
De Blob
Medal of Honor Heroes 2
The Godfather: Blackhand Edition
Klonoa
Mario Strikers Charged
One of the Raving Rabbids games
Games I hear good things about but haven't tried so can't make a call:
Little King's Story
NyzQuest
Sword and Soldiers
Muramasa
Cursed Mountain
Rabbids Go Home