Nokia 3310 LCD are still popular as they are simple to interface and you can find tons of software examples for various microcontrollers. But to push things further there is a nice instructable submitted by wkter. This time display is connected to AVR ATmega8 microcontroller that has software based USB (AVR-USB) that talks to PC.
This way you can easily send various messages or even graphics from any PC with libusb drivers installed. Anyway don’t expect much as USB is pretty slow, but ideal for displaying some information like feeds, tweets or other computer related information. Instructable is greatly explained and has all references needed to push forward.