Anthony Park has invented software that will allow you to browse the internet with the Media Center Edition remote. While not directly made for surfing on the Xbox360, we have put together just how to use it to do so. You can go to the more programs tab on your Xbox360 and run the program, then use the remote to surf the internet on your Xbox360.
NOTE: You NEED WindowsXP Media Center Edition, it will not work with Windows 2000 or any other form of Windows XP
Please note, while you are able to browse the Web, do not mistake this add-on to MCE or a full fledged Web browser. It is using the MCE PC to render an image of the Website which it displays on the 360, but you will not be able to enter any text. (For Example, google wouldn't be useful because you cannot enter text.) However you are able to follow links.
No, the USB Keyboard does not work with this as of yet. This also means the likelyhood of getting a virus on your Xbox360 is next to nothing. The browser is basically showing you an image of a browser running on your PC, so if your PC is protected, your Xbox360 is. The only way to exploit the Xbox360 would be with an image library exploit, we think.
[Props to gamersreports]