￼I am a member of the GRASS GIS development team.
The Geographic Resources Analysis Support System, commonly referred to as GRASS GIS, is a Geographic Information System (GIS) used for data management, image processing, graphics production, spatial modelling, and visualization of many types of data. It is Free (Libre) Software/Open Source released under GNU General Public License (GPL). GRASS is member project of the Open Source Geospatial Foundation.
Originally developed by the U.S. Army Construction Engineering Research Laboratories￼ (USA-CERL, 1982-1995), a branch of the US Army Corp of Engineers, as a tool for land management and environmental planning by the military, GRASS has evolved into a powerful utility with a wide range of applications in many different areas of scientific research. GRASS is currently used in academic and commercial settings around the world, as well as many governmental agencies including NASA, NOAA, USDA, DLR, CSIRO, the National Park Service, the U.S. Census Bureau, USGS, and many environmental consulting companies.
OSGeo Foundation site
Article discussing FOSS (free and open source software) for archaeology can be found here.