I was asked recently by some students what types of operations GIS Analyst/Developer are usually trying to automate by using Python with geoprocessing in ArcGIS and ArcPy site package. I guess it might be useful to know when searching for some exercises to do to be sure that what you create is relevant for the industry and might be re-used later already at the workplace.
The easiest answer would be "read the Esri help and go through the samples", but I was looking for more specific scenarios which are most common to implement. Thus, sharing workflows sush as "we are getting a .zip file with shapefiles, we use Python to unpack it, project them all to the X coordinate system, load into an ArcSDE geodatabase, grant users access to these data" are most welcome. Please feel comfortable to provide a concise description of the workflow, no extreme details are required.
Best Answer
For me, as your question suggests, I use Python a lot for automating batch processing in particular but also for creating any repeatable specialist calculations. These days I don't use ArcPy because I can't afford the ESRI licences as a freelance GIS Consultant. I use GDAL/OGR, Shapely, PostGIS, Numpy and SciPy a lot, though everything in my list could be done with ArcPy (and some of it was). Examples include:
Python in commercial geoprocessing is great because you have all the speed and brevity of scripting that Python provides and the speed of processing the compiled C-style code provides because, while Python is interpreted it is mostly calling compiled C-style code under the hood. Python provides the glue that can hold a lot of sequential geoprocessing tasks together and the list above is just a tiny snapshot of some of the things I personally use it for. In the 'Good Old Days' we would set up a Watch file and have ArcInfo record our command-line input and then clean up the AML (who remembers Arc Macro Language!) to make a reusable process of geoprocessing calls glued together with AML. It's not so different these days, except we use Python or C# as the glue.