Any ESRI boffins (insiders) know when this will be available? 2010, 2011?
FINAL UPDATE now released 20th January 2011 - Can be downloaded here - http://resources.arcgis.com/content/geodatabases/10.0/file-gdb-api (esri login required for legal/terms & conditions)
UPDATE:File Geodatabase API BETA in January 2011 >> http://blogs.esri.com/Dev/blogs/geodatabase/archive/2010/12/13/File-Geodatabase-API-details.aspx
Slighty dated is: When will you open access to the file geodatabase (without using ESRI software)?
We have been working to answer user requests for a way to access and use the file geodatabase without using ArcObjects. With the release of ArcGIS 9.4 [Now ARCGIS 10] next year, we will provide an open API for the file geodatabase
News: Beta begins in January 2011 (see answers below).