If you want to do it manually in ArcGIS, a possible solution would be to add a (temporary) column to your data set with the name - let's say - OVERLAP and a default value of 0. Then you query against the first layer (with select by location) and you update the OVERLAP column in the selection with the value 1. Then you repeat this step for the second layer, again using the value 1 to be put in OVERLAP. And again for any further layers.
At the end of this process you will be able to filter those polygons with OVERLAP still containing 0, i.e. those polygons that do not overlap with any of the other polygons.
What do you think of this suggestion?
Egge-Jan
P.S. Didn't see Dan's answer yet while I was writing mine.