As an example, on the left monitor, you could have your genealogy database open. On the right monitor, you could have the Internet open and view census images. If you find information in the right monitor, just copy and paste it into your application on the left.This is also a great solution for transcription projects: View a document image on one screen while typing into a word processor on the other.
If you have digital images on your computer, you could use the right monitor to view your digital image collection, while on the left you could preview one of the images at full screen.
[Photo credit: Muchos Monitors by reway2007]