I own two monitors. I finally gave in and set both up on the same computer. For work it has been okay, not worth going out and buying the second one though.
Genealogy is a very different story. Today on one monitor I had my genealogy program open to a family. On the other I had the Illinois Archives databases open. I was able to quickly check the dates for marriages and some deaths, Civil War and other military records where appropriate. I had a book open on the desk which sometimes had a different date than what I had entered probably 20 years ago and I wanted to see what the state said.
Illinois State Archives Databases
Without disturbing the open databases I could easily flip between people and families. Sometimes when they are sharing one screen one gets lost behind another window, accidentally closed, etc. With two monitors everything could stay open, full size, and visible at the same time.
Of course, it doesn't have to be the state archives. It could be ever growing FamilySearch.org or any other web site with information. On FamilySearch you can open some census records for example.
It is amazing the amount of time saved when you can enter the information directly into the program, enter the source, look back to verify if necessary and move on.
I wish I hadn't waited so long to convert to dual monitors.