I was curious and did some minor digging and found:
This article reveals the wireless chip from Broadcom to be BCM4318E
this press release from Broadcom says the Wii is using their 54g chip.
this link shows some info on the BCM4318E/802.11g chip.
Just a FYI, I've seen other posts speculating whether or not the Wii is b or g. Also, some users wondering if the g connection is truly g or just connecting with b through g. Hopefully this can make the issue a little more clear . I still have no clue why some people cannot connect when their router is on the g-only mode though.