So I've been really interested in doing something with twitter etc. so I've been doing alot of reading/research and I notice people are communicating with a local server through the USB. So my question is, besides being able to use the arduino away from the computer with the ethernet shield, what is the advantage to that over the USB? Say you had an old computer designated to handling this? Also does the ethernet allow me to access the arduino over the network? So if I'm on a laptop and build a web GUI can I control it over wireless network? lastly, does the ethernet vs USB make a difference if, for say, I wanted to use a remote host to control a local arduino? Is that even possible? Thanks guys.
Well you hit the nail on the head as relates to the computer. The advantage is that you don't need all the protocol stacks and such if you use serial USB communication to the Arduino. If you host the connection directly on the Arduino, then you will need the appropriate code to manage the connection and communication.
The arduino is capable of hosting a web interface with a network shield, and what capabilities you provide via that interface is up to you. Most ethenet intefaces "speak" SPI, wnich is a form of serial communications used between chips.
Take a look around, you can find examples of this within the forums and playground.