I have a polygon representing a wall.
How do I simplify this to a line representing the middle of the polygon using ArcGIS Desktop?
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I'm not sure which license level you have access to, but if you're working with an Advanced license for ArcGIS Desktop, you can use the "Collapse dual lines to Center line" tool (tool description here).
Alternatively, if you only have access to the Spatial Analyst extension, you could take the raster route by converting your polygon to raster, then using the "Thin" tool (tool description here) followed by a conversion back to a linear feature.
http://www.arcgis.com/home/item.html?id=bc642731870740aabf48134f90aa6165 (Polygon to Centerline Tool for ArcGIS) http://support.esri.com/technical-article/000012414 (How To: Create centerlines from polygon features)
We used these options to create road centerlines, basically the same process you need.