Yesterday I finally managed to get my Wii online and immediately installed Opera (after downloading R-Type). Quite a few websites get now Wii-friendly to work on the low resolution, with big chunky buttons and larger type.
Wiiflow for example has a collection of Flashgames, easily accessible - best of all, it has Zookeeper!
Finetunes is a music player specifically designed for the Wii, with a cover-flow-like interface.
And from Winksite you can download a WordPress plug-in to get your blog Wii-ready.