GDAL is a translator layer for raster spatial data. Includes multiple utility programs built-in, like gdalinfo (provides information of raster data), gdalwarp (wrap the raster in a new spatial reference), gdal_contour (build a contour file from an elevation raster), etc. Open Source.
OGR, included with GDAL now, provides a data abstration layer for vector-based spatial data. It includes some built-in utilities, like ogrinfo (provides information of vector data), ogr2ogr (translate vector data that ogr can read to vector data ogr can write), etc. Open Source.
A geophysical data manager developed by NOAA to support the collection, storage and retrieval of geophysical data. It can handle many data types like marine tracklines, hydrographic survey data, aeromagnetic data, etc. Free software.
An open-source cartographic projection procedures library. Python bindings available.
An open-source, Java library, that provides GIS functionality defined by Open Geospatial Consortium (OGC).
Spatial data extensions for the popular, open-source, Database Management System PostgreSQL. Open-source and well funded. Python libraries for accessing and using a PostGIS server are available.
A large collection of algorithms for computational geometry (including convex hulls, triangulation methods, spatial sorting, spatial searching, etc). Written in C/C++, but has Python bindings available.
Provides process-based, discrete-event simulation in Python. (A very good tutorial is here.)