I have been given some ESRI personal geodatabase files (MDB) and file geodatabase files (GDB). I don't know the coordinate system(s) for these files. Is there a way to do this without using ESRI software?
For feature classes in a file geodatabase you can use GDAL OGR. Be sure it has ESRI file geodatabase support which I think is GDAL version 1.9 or later. You can use the open version of File Geodatabase support this as well, I use this. MDB support in GDAL comes in via ODBC. QGIS will open the GDB and MDB files as well. Or you could just ask the person who gave you the files.