gvSig is a fairly popular open source mapping/gis cross-platform desktop client that is mostly funded by the Government of Spain. It is under the GPL license.
The underlying implementation is Java - JTS and GeneralPathX on top of Java 1.5.
Although we haven't used it extensively, many who have, swear by its speed compared to other open source desktop clients and say it handles huge shape files well. It also has some interesting extensions such as an ESRI ArcIMS client. Other popular formats it supports - PostGIS and MySQL spatial, HSQLDB, RASTER (tiff,jpg, MrSID,JPEG2000), Vector (ESRI SHP, dgn, dxf, GML), WMS WFS, WCS and AutoCad DWG version 2000, R14, R13, R12. Also allows editing of ESRI Shape and PostGIS data.
Pre-compiled installs available for Windows and Linux.