Yes, you can cruise around the web using your Xbox 360, and even transfer your favorite sites from your PC, but it takes a little bit of doing to make it happen. It works with a hack that you download and install on your PC. But it's not really a full-fledged Web browser, because what it's actually doing is rendering an image of each web page that you view on the XBox 360, so you won't be able to enter any text for Google searching or anything else. Only works with Windows XP Media Center Edition.
Browse The Internet On Your Xbox360 [Gamers Reports]