Finding open source GIS software is as simple as a Google Search.  Of course, once you do that, sorting through the hundreds of returns to find something useful, is likely to be a challenge.  If you look at the results for “open source GIS”, the first would seem likely.  That site, however, hasn’t been updated since 2008.  The 2nd return, QGIS is a much better bet.  As well, it will provide a link to what I consider the natural starting point for all open-source GIS hopefuls.That site is the Open Source Geospatial Foundation – www.osgeo.org.
Here is what the front page of their site says:

“Created to support and build the highest-quality open source geospatial software. Our goal is to encourage the use and collaborative development of community-led projects.”

Here is a quick run-down of the links and information available on the website.
The left side-bar is all about OSGeo.  There is information about the Foundation, blogs, a store, and an extensive user community.  In addition, there are translation pages for languages around the world.
The right side-bar contains the projects that OSGeo has a direct influence in, or is providing support for.  They are divided into the following sections:  Web Mapping; Desktop Applications; Geospatial Libraries; Metadata Catalog and Other Projects.
The middle section contains news and updates to a number of geospatial focused blogs.
There are a number of projects that are marked with a bullet.  These are projects that are being incubated by OSGeo.  This means that they are being given extra attention and funding to help develop them more quickly.
The programs that I am using that are referenced here include:  Quantum GIS – Desktop Mapping; GDAL/OGR – Geospatial Libraries; and OpenLayers, MapServer and Geoserver – Web Mapping.
There is a great deal of information about each project available through the various links.  I encourage you to check them out and develop your own open source GIS software suite.