Creating polygon feature class from area in one not covered by another using ArcGIS Desktop?

Erase is the tool for this in ArcGIS.

http://resources.arcgis.com/en/help/main/10.1/index.html#//00080000000m000000

Kind of like an "opposite clip"

You need a higher level license to do this.

If you don't have an info level of license you can do it using union, which is limited to two feature classes in basic and standard, but that's enough.

Union your two layers, to keep it simple join the attributes with FID only, and then delete the ones that have a FID value from the second feature class. There are a few ways to delete but if you wish to do this in a model make a feature layer with an appropriate where clause and use delete features to remove the unwanted areas.

The ArcGIS Erase tool will work, but as user two seven three nine says, you have to have the required license level to use it. The Xtools Pro extension suite has an Erase tool built in that will do the same thing and is free. Some of the features of Xtools require that you buy a license after the 14-day evaluation period is over, but the Erase tool (and a ton of other very useful ones) is free to use forever.