Absolutely YES. You can simply softmod your Xbox with various methods, whichever is most available to you. I suggest using the UnleashX softmod. You need but google it or browse these forums to figure out how to install it.
You're going to need an FTP CROSSOVER cable in order to add media to your xbox, avi, flv, mp3, etc. You will most likely be using a great program called XBMC, which can even connect to Youtube.
You can even install Linux and/or Win98 emulation, both with internet capabilities. For something so cheap off ebay, it's easily turned into a machine worth over 200$.
Only downside is the original HD for Xbox is sadly 8gb or 10gb (depends on model, I HIGHLY reccommend you buy a NON 1.06 Xbox). However, with your softmod installed, upgrading to let's say a 500gb HD is nothing but carefully followed steps. If you need any help feel free to ask.
