Convert Postscript (*.ps), Encapsulated Postscript (*.eps), or Adobe Illustrator (*.ai) files to shapefile?

I don't think I've ever seen such a beast. I use several tricks though. Scan2cad will convert a vector pdf to dxf. So the 3 step process I have used.

1. convert the ai,ps,eps to pdf with adobe acrobat.
2. convert pdf to dxf with scan2cad.
3. covert dxf to shp with arcmap.

rather ugly but it works

You can convert PS to TIff using GhostScipt or IrfanView. If you georeference the Tiff first, creating a Geotiff or a world file, you should also assigned a coordinate system (gdal_translate -a_srs). Then you can run gdal_polygonize.py to convert the geoTiff to a Shapefile. The shapefile coordinates should match the geotiff.

If you have Adobe Illustrator, there is an add-on (not free) called MaPublisher. It adds some GIS capabilities to Illustrator. In addition, it adds some export functionality including export to shapefile.

I'm surprised that FME doesn't have the ability to read to these formats, but it can write to them.