my bro-in-law is using the wireless network adapter on the 360 and a linksys wrt54g to connect to the intertubes and xbox live and has had no issues.
fwiw, i'm using a hacked linksys wrt54g acting as a wireless bridge instead of the wireless network adapter for my 360 and i have the verizon wireless router/modem to connect to the intertubes (and xlive).