As we know esri shared their library which makes it possible to work with FileGDB format without using ArcObjects. So the question is what kind of applications could be created in order to help GIS specialist to solve their tasks related with this format? For instance, I have an idea to create an opensource tool(GPL) which converts FileGDB to Shapefile (or other format) and backwards. Will it be in the demand? or perhaps somebody have already developed such tool? I will be grateful for any ideas about that (as well as collaboration ideas).
If you're planning to work in the Open Source world, I highly recommend looking at GDAL as a jumping off platform.
"GDAL is a translator library for raster geospatial data formats that is released under an X/MIT style Open Source license by the Open Source Geospatial Foundation. As a library, it presents a single abstract data model to the calling application for all supported formats. It also comes with a variety of useful commandline utilities for data translation and processing." -- http://gdal.org/
The library has support for dozens of formats beyond shapefiles, and there is already experimental support for the File Geodatabase using ESRI's APIs.
Strong support for File Geodatabase in GDAL would allow users to use these files in a myriad of open source tools -- MapServer, qgis, GRASS, etc. -- that use GDAL/OGR as an underlying data provider. (Note that ESRI itself uses GDAL as a translation layer to many image formats, and a way of extending ESRI's image processing support is to write a GDAL plugin.)
Also note that your idea of creating such a tool under the GPL is impractical, because ESRI's library can not be released under the GPL, the final product could not be distributed (as it would be in the violation of the GPL).
I will just add to crschmidt's reply that GDAL already has experimental support for the FileGDB API, too. It is just not compiled by default.
A few limitations is that it only works for points and it is readonly. Both things that can be changed - and patches are welcomed :)