I've been using dual monitors for years with ArcGIS. A lot of the benefit is not so much in splitting the actual software over two monitors, but instead, to use it on one monitor and other programs on the 2nd monitor.
Here is my current setup.
Monitor 1: Outlook, Windows Explorer, ArcGIS Attribute Tables, MS Access, etc
Monitor 2: ArcGIS Data/Layout View, Firefox, etc
I tend to have more than one instance of ArcGIS running at a time, so I will sometimes split them between monitors so that I can easily see both for reference or copy layers between the two.
If you are using ArcGIS 10, you have the option of having the Catalog window docked in your data view. It is still possible to have that open as a separate program, and you could move that to the opposite window for easy access.
You can do something similar with ArcToolbox. Either have it docked, or undock and move to a different window.
The long and short of it is, you have to play around with different configurations to see what works the best for you. Don't think of just ArcGIS when you think of your dual monitor setup, but consider it as part of your overall software workflow.