I gave this one star on the hope that people will read this and ignore the 'doesn't work' post, or at least consider what sort of installation they have. Any USB-Ethernet connector should work fine, just get one from a reputable supplied like Amazon or a shop.
There is a misunderstanding and conflict of comments regarding internet connecions.
If you have a DSL modem and plug your PC directly into it, and it, in turn, connects to the internet without any setup, you may be prompted to enter your username and password if you have what is known as a PP0E connection. As the Wii does not have this option, these type of connections cannot work whereas a PC does have the ability to enter a username and password.
I suspect most people have an ADSL/Router of one make or another. These usually have a number of ports in the back (all mine have 4) to allow multiple devices to connect to the internet at the same time from your devices. The ADSL/Router needs to be set up correctly and your ISP should have given you instructions, it's usually in the documentation of the router and the ISP specifies any specifics that you need. ADSL/Routers have a way of getting a PC to configure using a web browser.
So, as long as you have an ADSL Router then the Wii will not know (nor care) how the ADSL/Router is configured. If you don't have one and then I would suggest buying one that works for your ISP and has multiple ports. Wireless ADSL/ROuters are pretty cheap and with 4 ports you can leave the PC connected and connect the Wii (have a look at Homeplug if things are in different rooms and you want to avoid wireless for some reason).
I hope the above explains why someone said it doesn't work (they either don;t know how to set up a ADSL/Router, or don;t have one) and the attached comment said they their works fine (they will have an ADSL /Router like I do.