ArcExplorer (http://www.esri.com/)
Quantum GIS (QGIS) (http://qgis.org/)
Thuban (http://thuban.intevation.org/)
gvSIG (http://www.gvsig.gva.es/)
More applications can be found at FreeGIS.org

ArcExplorer:

I downloaded the ArcExplorer 9.3-Java Edition for Windows.  Before you can download, you're reqiured to register (it is free).  The download is large (60Mb), so go fix yourself a cup of coffee before we start...  

Installation is straight forward.  You need to unzip the file you just downloaded and then double-click on the AEJaveSetup.exe file to start the install process.  Unless you know what you are doing, I suggest you accept the defaults during this process.  When complete, you'll have a new item in your Programs list (Start > All Programs > ArcGIS > ArcExplorer Java Edition).  Fire it up, and lets go...