Is it possible to open a Personal Geodatabase file in software other than ArcGIS?
i.e are there any open source software available just for viewing the data?
It can be viewed in Quantum GIS, a popular open source desktop gis application.
Layer > Add Vector Layer and select Personal Geodatabase from File Types.
It will display all feature classes. But advanced ESRI features like Network and Topology will not be visible.
You can open a PGDB in Microsoft Access if you have it as it's just an access database.
If you need opensource then you could use OpenOffice
The free TatukGIS viewer will open ESRI personal geodatabases. It is not open source.
As a side note, as you mentioned just being able to view the files only. You could try exporting to a layer package file.
The layer package derived from personal databases or layers contained therein, can be viewed in free software like ArcGIS Explorer (http://www.esri.com/software/arcgis/explorer-desktop/download).
This is useful if people need to view files, but do not have access to an ArcGIS Licence.
I don't know if that is exactly what you needed. But, hopefully the information is useful.