Yes, you can. You require either a wireless router running 802.11 b/g, or a USB-to-LAN adaptor that is purchasable separately, and then you get some regular CAT5 cable to connect into a regular router.
If you just have an ADSL modem, you will need to get yourself a router.
Another option is the WiFi USB connector - stick this into your internet-connected PC and it acts as an access point for the Wii
See here for more details:
http://wii.nintendo.co.uk/54.html copy