Why might the windshield wipers in a 1993 Chevy Suburban not work?

There are a number of possibilities. Wiper motors often fail and you'll get nothing. Check to see if power is getting to the motor when you turn on the switch. Understand that there are two wires that go to the wiper that can have power. One is powered any time the keyswitch is on, the other only gets power when the wiper switch is on. If both are working right, it just about has to be the motor. There may be cracked solder joints in the wiper motor/controller assembly. this was a common problem recalled by GM. If you remove the cover from the wiper motor (no need to dismount the motor from the vehicle) you will see a circuit card. Check all the solder joints for cracks, parcticularly those on the connector for the wiring. The cracked joints can easily be repaired with a soldering iron.