I just got introduced to this site, and am not versed in GTD. Nonetheless, I'm guessing that it involves some sort of linkages of actions to goals, or something similar. FileMaker, as a very powerful relational database that can be run on personal computers, is a perfect tool for this kind of setup. I'm working on such a database right now. That said, to properly setup a worthwhile relational database takes some non-trivial learning. Anyone wishing to pursue their own GTD database *and* to learn FileMaker, including its relational capabilities, could build something very useful; it will likely take some time though to do it well. Or you might be able to find an existing database that could be used for GTD.
The second point is that FileMaker has a mobile app, FileMaker Mobile 7, which I run on my Palm. It is quite useful being able to sync FileMaker Pro (desktop) databases, however it is not relational, and has very little of the power of FileMaker Pro, such as scripts, etc., etc. You can run scripts in FileMaker Pro prior to syncing to a PDA, which is useful, but your mobile databases will always be flat file. It is challenging to merge the capabilities of the desktop app with the mobile app.
Good luck and update this forum if you learn anything useful to share!