You use USB ports to connect Arduino to the PC.
Then on the PC a VIRTUAL serial port is established for each Arduinio bord connected to the PC.
So you do not need a PHYSICAL serial port for each Arduino board, just a USB port.
I don't know how many Arduinos you can connect via USB. I have only tried two at the same time.
You can connect the Arduino to a Ethernet device with something like Lady Ada's Ethermet shield for Arduino : http://www.adafruit.com/index.php?main_page=product_info&cPath=17_21&products_id=83&zenid=17d891c69840ba3c0791af1a91a37f30
But the shield and the Xport module would cost more than 40$ for each Arduino board
There are other Ethernet to Serial modules available as well