In the geospatial world a directory ending in .gdb is usually the Esri File Geodatabase Format, which finally has an open API which many 3rd party programs can read -- GDAL/OGR, FME and GlobalMapper to name the ones I'm familiar with. Gdal/ogr is open source and is included in many other applications like Quantum GIS and SAGA. The gdal/ogr FileGDB driver is not included by default as the Esri SDK needs to be downloaded and installed separately.
A file ending in .gdb is likely the Garmin GPS Database format used by MapSource and Basecamp and the open source gpsbabel can read it, see Batch converting Garmin GDB to GPX?.