Ethernet is a low voltage, low current system designed to be "hot plugged", so nothing should happen beyond the computer losing its Internet connection.
Why do you ask? What is your concern?
Thanks Bruce. I just had a new Gateway modem installed and became kind of paranoid of being connected to the internet when the computer is at idle and possibly being hacked. I though that if I unplugged the Ethernet cable it would disconnect me from the internet, but I wasn't sure if it would do any damage to the modem or if it would have to be reset. Thanks again.....Lee.