The ethernet connector on the xbox is the standard RJ45 connector that you see on most twisted-pair ethernet. It will plug into the LAN ports on your router no problem.
muleo, if you have vodafone ADSL broadband over your home phone line -- only offered since mid-2008 -- it should work (aside from a minority of routers have problems with xbox, and I can't say for the Vodafone-supplied one). If you are talking about Vodafone's mobile broadband via that little compact USB modem they sell, no it will not work because a) it is a modem, not a router -- you would need a quite complicated (and expensive) setup using a separate computer as a router and bridge between your USB broadband connection and a wired/wireless network, b) even if you did that the latency on a mobile broadband connection is usually much too high for gaming -- I've measured it as being approx. a factor of 4-20 higher. Plus, mobile broadband throughput is dependent on where you are, how many other users are using it, and can be highly variable at different times even in a single location.
For someone with a normal wired router or the common wireless ones which also have 4 wired LAN ports, another option instead of buying a wireless adapter for the xbox is to buy a wired extender kit, which will let you run ethernet over the electrical wiring in your house. You have two devices which plug into electric wall sockets. One connects to your wired router in one room, the other to the xbox in another. In houses with not-so-good wiring it is possible to have noise on the electric wiring which interferes with this type of signal, but it should work for most people.