Open Source Tool capable of reading Esri File Geodatabase (.gdb)?
In the geospatial world a directory ending in .gdb is usually the Esri File Geodatabase Format, which 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 QGIS and SAGA.
Windows end users can most easily get the filegdb driver via the OSGeo4W gdal-filegdb
package.
For developers, the gdal/ogr FileGDB driver is not included by default as the Esri SDK needs to be downloaded and installed separately (see build instructions).
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?.
No. .gdb is a proprietary format and ESRI isn't sharing the spec or providing an API.
I believe that some people have been able to hack together something to pull the features out, but none of the relationships, topology, domains, etc.
The best way to get the features out would be to dump the database to a shapefile or a ESRI personal database. The OGR library and tools can read personal geodatabases.
The next version of ogr will support reading file geodatabases. More info here: http://trac.osgeo.org/gdal/ticket/3332
Edit: In the meantime it is present in gdal/ogr: http://gdal.org/drv_filegdb.html